Question

Find the last term and the number of terms.
number n of terms in a geometric progression {an), if a-3.
ar - 96 and S-189​

Answer 1

Answer:

For a G.P an=a1rn−1 where r is common ratio.

Given that an=96

⇒3×rn−1=96

⇒rn−1=32

⇒rn=32r      [Let this be equation 1]

Also, sum of the first n terms of a finite G.P. is given by Sn=r−1a1(rn−1)

⇒r−13(32r−1)=189

⇒32r−1=63r−63

⇒31r=62

⇒r=2

Putting r=2 in equation 1,we  get

⇒2n=64

⇒n=6

⇒32r−1=63r−63

⇒31r=62

⇒r=2

Putting r=2 in equation 1,we  get

⇒2n=64

⇒n=6

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