Question

find the 9th term and nth term of the GP 1/4, -1/2, 1, -2......​

Answer 1

Step-by-step explanation:

Given GP is

1/4, -1/2, 1, -2.........

Now,

a = 1/4..,

Common ratio =r = a2/a1 = a3/a2

= -1/2/1/4 = 1/-1/2

= -1/2 = -1/2

:. Common ratio = -1/2

Now Consider,

9th term of GP,

W.K.T,

_________

an = a.r^n-1

_________

a9 = (1/4).(-1/2)^9-1

a9 = (1/4).(-1/2)^8

a9 = -1/8^9

:. a9 = -1/8^9

Now Consider,

nth term of GP,

W.K.T,

__________

an = a.r^n-1

__________

an = (1/4).(-1/2)^n-1

an = (1/4).(-1/2)^n

an = -1/8^n

:. an = -1/8^n

Therefore,the 9th and nth term of GP is -1/8^9, -1/8^n.

Hope it Helps,

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