Question

in a G.p the 3rdterm is 24 and 6th term is 192 find the 10th term​

Answer 1

Answer:

3rd term of the GP = 24 = ar2

6th Term of the GP = 192 = ar5

.

Hence,

6th term / 3rd term = ar5 / ar2 = 192 / 24

r3 = (192) / (24)

r3= (2*2*2*2*2*2*3) / (2*2*2*3) = (23)

Hence, r = 2

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Since, ar2 =24

a(2)2 = 24

a = 24/4 = 6

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Hence first term, a = 6, and r = 2.

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Hence, the 10th term = ar10-1 = ar9

10th term = (6)(2)9 = 6(2)8 (2) = 6(4)4 (2) = 6(16)2 (2) = (6)(256)(2) = 3072,

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Hence the 10th term = 3072.