Find the 17th and nth terms of the GP 2, 2√2, 4, 8√2….
Given GP is 2, 2√2, 4, 8√2 …..
The given GP is of the form, a, ar, ar2, ar3….
Where r is the common ratio.
First term in the given GP, a1 = a = 2
Second term in GP, a2 = 2√2
Now, the common ratio,
Now, nth term of GP is, an = arn – 1
So, the 17th term in the GP,
a17 = ar16
= 2 x (√2)16
= 512
nth term in the GP,
an = arn – 1
= 2(√2) n – 1
= (√2) n + 1
Hence, 17th term = 512 and nth term = (√2) n + 1