Q19 of 97 Page 192

Find the sum of the products of the corresponding terms of the sequences 2, 4, 8,16, 32 and 128, 32, 8, 2,

Given: the sequences are 2, 4, 8,16, 32 and 128, 32, 8, 2,


The Required answer is: 2 × 128 + 4 × 32 + 8 × 8 + 16 × 2 + 32 ×


⇒ 64 × [4 + 2 + 1 + + ]


Here the terms are in G.P


Where a = 4, r = and n = 5


The Sum of terms in G.P. is given by:


∴ S = 64 ×


⇒ S = 64 ×


⇒ S = 64 ×


⇒ S = 2 ×


⇒ S = = 496


∴ The required answer is 496.


More from this chapter

All 97 →
17

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.

 18

Find the sum to n terms of the sequence 8, 88, 888, 8888… .

 20

Show that the products of the corresponding terms of the sequences a, ar, ar2,…arn – 1 and A, AR, AR2, … ARn – 1 form a G.P, and find the common ratio.

 21

Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.