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 C. 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) E. All of these 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 B. 112/15 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 [su_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