Question

17. Which term of the A.P. 2, 8, ..... is 512 ?
10​

Answer 1

Step-by-step explanation:

Let the first term be 'a'

The common difference be 'r'

nth term is = a*r^(n-1)

So

first term

a1 = a*r^0

a = 18

second term

a2 = a*r^1 = -12

hence r = -2/3

Third term

a3 = 18*(-2/3)^2

= 8

Hence

a = 18

r = -2/3

512/729 = 18*(-2/3)^n -------(1)

after cross multiplying 18 we have to find the power of n which satisfies (-2/3)^n = 256/6561

we obtain (-2)^8 = 256 and 3^8 = 6561

therefore (1) becomes

18*(-2/3)^8 = 512/729

n-1 = 8

Therefore it is the 9th term

Answer 2

Step-by-step explanation:

the answer is 86 term

hi