Question

An geometric progression has t1 = 12 , r = 1/2 , and tn = 3/8 . Find n and Sn.

Answer 1

Step-by-step explanation:

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If in a G.P. {a

n

},a

1

=3,a

n

=96 and S

n

=189 then the value of n is

Medium

Solution

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Correct option is B)

For a G.P a

n

=a

1

r

n−1

where r is common ratio.

Given that a

n

=96

⇒3×r

n−1

=96

⇒r

n−1

=32

⇒r

n

=32r [Let this be equation 1]

Also, sum of the first n terms of a finite G.P. is given by S

n

=

r−1

a

1

(r

n

−1)

⇒

r−1

3(32r−1)

=189

⇒32r−1=63r−63

⇒31r=62

⇒r=2

Putting r=2 in equation 1,we get

⇒2

n

=64

⇒n=6