Question

find the Gp where 7th term is 320 and 10th term is 2560

Answer 1

this is your required solution

Answer 2

The GP has first term 10 and a common ratio of 2

Given,

7th term of GP = 320

10th term of GP = 2560

To Find,

the GP

Solution,

A geometric progression, often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

We know that the nth term of a GP is given by Tn = ar^(n-1),

where a = the first term, and r = the common ratio of the GP

7th term of the GP = ar^6

⇒ ar^6 = 320 (equation 1)

10th term of the GP = ar^9

⇒ ar^9 = 2560 (equation 2)

Divide the LHS and RHS of equation 1 by equation 2:

⇒ (ar^6)/(ar^9) = 320/2560

⇒ 1/r^3 = 1/8

⇒ r^3 = 8 = 2^3

⇒ r = 2

Now, from equation 1,

⇒ ar^6 = 320

⇒ a × 2^6 = 320

⇒ a × 32 = 320

⇒ a = 10

Therefore, the given GP has first term 10 and a common ratio of 2

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