## Series and Parallel Sequences MCQs

**1: G1,G2,…,Gn are said to be n geometric means between a and b if a,G1,…Gn,b is called ______________. Select the correct option.**

A. A.P

B. a sequence

C. not a sequence

D. G.P

E. All of these

F. Both A and B

**2. If H,G,A are arithmetic, geometric and harmonic means between b and a respectively, then H,G,Aare______________. Select the correct option.**

A. Real numbers

B. in G.P

C. in A.P

D. in H.P

E. All of these

F. Both A and B

**3: Common difference of sequence 5,8,11,14,… is called ______________. Select the correct option.**

A. 3

B. −3

C. 0

D. 1

E. All of these

F. Both A and B

**4: Arithmetic mean between 2+√(2) and 2-√(2) is called ______________. Select the correct option.**

A. 4

B. 2

C. √(2)

D. 0

E. All of these

F. Both A and B

**5: 2¹ + 2² +2³ +….+2n =______________. Select the correct option**.

A. 2(2n+1 -1)

B. 2(2n – 1)

C. 2(2n-1 -1)

D. None of Above

E. All of these

F. Both A and B

**6: Fifth term of sequence an = 2n+3 is called _______________. Select the suitable option.**

A. 13

B. −13

C. −7

D. 7

E. All of these

F. Both A and B

**7: 5th term of G.P 3,6,12,… is called _______________. Select the suitable option.**

A. 3

B. 15

C. 48

D. 2

E. All of these

F. Both A and B

**8: A.M between 3√(5) and 5√(5) is called _______________. Select the suitable option.**

A. 4√(5)

B. √(5)

C. 2√(5)

D. 3√(5)

E. All of these

F. Both A and B

**9: A.M between 1-x+x² and 1+x+x² is called _______________. Select the suitable option.**

A. 1+x²

B. 2-x²

D. 1-x²

E. All of these

F. Both A and B

**10: Series obtained by adding term of arithmetic sequences is called _______________. Select the suitable option.**

A. infinite series

B. harmonic series

C. geometric series

D. arithmetic series

E. All of these

F. Both A and B

**11: Sum of series 1+1/3+1/3² +… is _____________.which of the following is a suitable option.**

A. 10⁄9

B. 2

C. ³⁄2

D. 4⁄3

E. All of these

F. Both A and B

**12: If A and H are arithmetic and harmonic mean between 2 and 3, then A + H = _____________.which of the following is a suitable option.**

A. 32/4

B. 49/20

C. 49/10

D. 49/5

E. All of these

F. Both A and B

**13: A.M between 9 and 11 is _____________.which of the following is a suitable option.**

A. 0

B. 10

C. 9

D. 5

E. All of these

F. Both A and B

**14: Sum of first 15th terms of series 3+19+35+… is _____________.which of the following is a suitable option.**

A. 23

B. 1725

C. 345

D. 69

E. All of these

F. Both A and B

**15: 2,4,6,8,10,12,… is called _____________.which of the following is a suitable option.**

A. arithmetic series

B. G.P

C. A.P

D. Geometric series

E. All of these

F. Both A and B

**16: No terms of a Harmonic sequence can be ____________.Choose the correct option**.

A. 0

B. 1

C. 2

D. 3

E. All of these

F. Both A and B

**17: If n is the total number of harmonic mean between x and then mth harmonic mean between x and y is ____________.Choose the correct option.**

A. (n+1)ba

B. (n+1)ab/(n+1)+n(a-b)

C. (n+1)ab/(n+1)b+m(a-b)

D. (n+1)b+m(a-b)

F. Both A and B

**18: 2nd term of sequence with general term n² – 4/2 is ____________.Choose the correct option.**

A. 0

B. 3

C. −3

D. 1

E. All of these

F. Both A and B

**19: Sum of 1st 6 terms of series 1+7+13+… is ____________.Choose the correct option.**

A. 96

B. 12

C. 24

D. 48

E. All of these

F. Both A and B

**20: H1,H2,…,Hn are said to be n harmonic means between x and y if x,H1,H2…,Hn,y form ____________.Choose the correct option.**

A. Harmonic series

B. H.P

C. A.P

D. G.P

E. All of these

F. Both A and B

**21: If a and d are first term and common difference of A.P respectively, then nth term of corresponding H.P is _____________. Select the correct option.**

A. an = a/a+(n-1)d

B. an = a+(n-1)d

C. an = 1/a+(n-1)d

D. an = a/1+(n-1)d

E. All of these

F. Both A and B

**22: If n is the total number of G.M between a and b than nth geometric mean between a and b is _____________. Select the correct option.**

A. ab

B. a(b/a)n/n+1

C. a(b/a)m/n+1

D. b(a/b)m/n+1

E. All of these

F. Both A and B

**23:Common ratio r is _____________. Select the correct option.**

A. r ≤ −1,r≥ 1

B. −1 < r < 1

C. −1 ≤ r ≤ 1

D. r < −1,r > 1

E. All of these

F. Both A and B

**24: Sum of series 1+1/2+1/2² + … is _____________. Select the correct option.**

A. 10⁄9

B. 2

C. ³⁄2

D. 4⁄3

E. All of these

F. Both A and B

**25: 1,8,15,22,29,36,… is _____________. Select the correct option**.

A. arithmetic series

B. G.P

C. A.P

D. Geometric series

E. All of these

F. Both A and B

**26: A.P whose nth term is 2n-1 is _____________. Which of the following is a correct option?**

A. 5,3,1,…

B. 1,3,6,…

C. 2,3,5,…

D. 1,3,5,…

E. All of these

F. Both A and B

**27: Arithmetic mean between a and b is _____________. Which of the following is a correct option?**

A. ±√(ab)

B. a-b/2

C. b-a/2

D. a + b/2

E. All of these

F. Both A and B

**28: If an+2 + bn+2/an+1 + bn+1 is geometric mean between a and b, then n = _____________. Which of the following is a correct option?**

A. −0.5

B. −1

C. 1

D. −2

E. All of these

F. Both A and B

**29: A number G is said to be geometric mean between 2 numbers a and b if a,G,b is_____________. Which of the following is the correct option?**

A. G.P

B. a sequence

C. A.P

D. not a sequence

E. All of these

F. Both A and B

**30: Geometric mean between -2ι and 8ι are _____________. Which of the following is a correct option?**

A. ±1

B. ±4

C. ±3

D. ±2

E. All of these

F. Both A and B

**31: A.M between x-3 and x+5 is called _______________. Select the correct option.**

A. 2x+2

B. x-1

C. x+1

D. 2x-1

E. All of these

F. Both A and B

**32: Harmonic mean between two numbers a and b is _______________. Select the correct option.**

A. 2ab/a-b

B. a+b/2ab

C. a-b/2ab

D. 2ab/(a+b)

E. All of these

F. Both A and B

**33: Series obtained by adding terms of geometric sequences is called _______________. Select the correct option.**

A. infinite series

B. harmonic series

C. geometric series

D. arithmetic series

E. All of these

F. Both A and B

**34: If H is harmonic mean between 7 and 8, then H/2 = _______________. Select the correct option.**

A. 14/15

C. 56/15

D. 28/15

E. All of these

F. Both A and B

**35: 1/2,1/7,1/12,… is _______________. Select the correct option.**

A. a harmonic series

B. an arithmetic progression

C. a Geometric Progression (GP)

D. a harmonic progression

E. All of these

F. Both A and B

**36: If an+1 + bn+1/an + bn is harmonic mean between a and b, then n = ________________. Select the suitable option.**

A. 0

B. −1

C. 1

D. −2

E. All of these

F. Both A and B

[s**u_spoiler title=”Answer – Click Here:” class=”padding: -10px;”]D[/su_spoiler]**

**37: A geometric mean between 2 and 4 is ________________. Select the suitable option.**

A. ±√(2)

B. ±8√(2)

C. ±4√(2)

D. ±2√(2)

E. All of these

F. Both A and B

**38: Twice sum of 1st fifteen terms of series 5+10+20+ … is ________________. Select the suitable option.**

A. 10230

B. 341

C. 1023

D. 5115

E. All of these

F. Both A and B

**39: 5th term of and nth term of A.P 1,5,… are ________________. Select the suitable option.**

A. 17,4n

B. 17,4n-3

C. 4n-3,17

D. 17,3n-4

E. All of these

F. Both A and B

**40: 2 geometric means between a and b are ________________. Select the suitable option.**

A. ab

B. a(b/a)1/2,b

C. a(a/b)1/2,b

D. a(b/a)1/2,b

E. All of these

F. Both A and B