Question

1,-1/2,1/4..
are in GP.. then find 8th term.​

Answer 1

Answer:

r=2

a

8

=a

1

(2)

8−1

192=a

1

(2)

7

192=a

1

(2)

7

2

7

192

=a

1

2

7

192

×2

12−1

=a

12

2

7

192

×2

11

=a

12

a

12

=192×2

4

a

12

=3072

Answer 2

Question :-

1,-1/2,1/4 are in GP . then find 8th term. ?

Solution :-

→ First Term of GP = a = 1

→ Common Ratio = Second Term / First Term = (-1/2) / 1 = (-1/2)

we have to find 8th term of this GP.

we know that, The nth term of a GP series is Tn = a*r^(n-1), where a is first term and r is common ratio.

So,

→ a = 1

→ r = (-1/2)

→ n = 8

Putting all values we get :-

→Tn = a*r^(n-1)

→ T(8) = 1 * (-1/2)^(8 - 1)

→ T(8) = (-1/2)^7

→ T(8) = (-1)^7 / (2)^7

→ T(8) = (-1) / 128

→ T(8) = (-1/128) (Ans.)

Hence, 8th term of the GP is (-1/128) .

___________________

Extra :-

→ sum of n terms of GP = a[(1 - r^n) / (1 - r)]

→ sum of infinite terms of GP = a/(1 - r)