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Sequence & Series - 3
Choose the correct alternative. Only one choice is correct.
1.
Sum of n terms of series : x y x 2 xy y2 x3 xy2 x 2 y y3 . . . . .
(1)
x 1 x y 1 y
2 n 2 n
(2)
2
1 x 1 x
n
y2 1 yn
xy xy x y 1 x 1 y
(3)
x2 1 xn y 1 y
2 n
(4) None of these
1 x 1 y
n n
2. If
I r 3r 1 , then I r is equal to :
1
r 1 r 1
1 n 1 n 3 1
n
(1) 2 1 (2) 1 (3) 1 (4) None of these
3 3 4 3
3. Let positive numbers a, b, c, d be in A.P. then abc, abd, acd, bcd are :
(1) not in A.P. or G.P. or H.P. (2) in A.P. (3) in G.P. (4) in H.P.
4. If a2, b2, c2 are in A.P., then b + c, c + a, a + b are in
(1) A.P (2) G.P. (3) H.P. (4) None of these
5. The harmonic mean and geometric mean of two positive numbers are in the ratio 4 : 5, then two numbers are in the ratio.
(1) 4 : 1 (2) 3 : 1 (3) 2 : 1 (4) 1 : 3
6. Sum of integers from 1 to 100 that are divisible by 2 or 5 is :
(1) 3050 (2) 3150 (3) 3250 (4) None of these
7. If x > 0 and log2x log2 x log2 4 x log2 8 x +. . . . . . = 4 then x equals:
(1) 2 (2) 3 (3) 4 (4) 5
8. If the sum of first 2n terms of the A.P. 2, 5, 8, . . . . is equal to the sum of first n terms of the A.P. 57, 59, 61 . . . . . then n equals
(1) 10 (2) 12 (3) 11 (4) 13
9. If first, second and last term of an A.P. are a, b and 2a respectively, then its sum is
(1) ab (2)
ab (3) 3ab (4) None of these
2(b – a) b–a 2(b – a)
10. The sum Sn to n-terms of the series
1 3 7 15
.... is equal to
2 4 8 16
(1) 2n – n – 1 (2) 1 – 2-n (3) 2–n + n – 1 (4) 2n – 1
