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Find a G.P. for which sum of the first two terms is -{4}and th

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Find a G.P. for which sum of the first two terms is $- 4$ and the fifth term is 4 times the third term.

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Find a G.P. for which sum of the first two terms is

- 4

and the fifth term is 4 times the third term.

13 mins ago

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13 mins ago

Text solutionVerified

Solution: given that ,

a + a r = - 4

eqn(1)

T_{5} = 4 T_{3}

a r^{4} = 4 a r^{2}

r^{2} = 4

r = \pm 2

now

a (1 + r) = - 4

r = 2, a = - \frac{4}{3}

- \frac{4}{3} + (- \frac{8}{3}) + (- \frac{16}{3}) \dots\dots ..

r = - 2, a = - \frac{4}{- 1} = 4

4 + (- 8) + 16 + (- 32) \dots\dots .

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Question Text	Find a G.P. for which sum of the first two terms is $- 4$ and the fifth term is 4 times the third term.
Answer Type	Text solution:1
Upvotes	150