Question

The 8th term of a GP is 16 times the 4th term. What will be the first term when its sixth term is 64.?

Answer 1

Answer:

The first term of GP is = 2

Step-by-step explanation:

Let the first term of the GP is = a [a not equal to zero]

and the common ratio of the GP is = r

So, the 4 th term of the GP is = a×r^(4-1) = a×r^3

And the the 8th term of the GP is = a×r^(8-1) = a×r^7

And the 6th term of GP is = a×r^5

Now by given condition,

a×r^7= 16×a×r^3

=> r^7 = 16× r^3 [ a is cancelled out as a is not equal to zero]

=>r^4 = 16

=> r^4 = 2^4

=> r = 2

And we know the 6 th term of the GP is = 64

So, a×r^5 = 64

=> a × 2^5 = 64

=> a×32 = 64

=> a = 64÷32=2

So, a = 2

Therefore the first term of the GP is = 2