Question

The first term of a G.P 3 and its last term is 192 .Also the sum of the given series is 129 .find the number of term in the G.P.​

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Secondary School Math 5 points

The first term of a G.P 3 and its last term is 192 .Also the sum of the given series is 129 .find the number of term in the G.P.

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keyurbhoj

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Answer: 7

Step-by-step explanation:

the GP can be written as a, ar, ar^2, ar^3...ar^(n-1)

now a=3 , ar^(n-1) = 192. taking ratio of both

ar^(n-1)/a = 192/3

r^(n-1)= 64 ......equation 1

now, sum = a* (r^n-1)/(r-1)

129 = 3* (64r-1)/(r-1) [ r^n = r*r^(n-1)=r*64=64r]

43 (r-1) = 64r - 1

43r - 43 = 64r -1

-21r=42

r = -2

now from equation 1

r^(n-1)= (-2)^(6)

n-1 = 6

n = 7