Answer:
the first term of the GP is 17/16 and the common ratio is 2.
Explanation:
Let the first term of the GP be "a" and the common ratio be "r". Then, according to the formula for the nth term of a GP, we have:
5th term = a r^4
7th term = a r^6
We are given that the 5th term is 17 and the 7th term is 68. Substituting these values into the above equations, we get:
17 = a r^4 ...(1)
68 = a r^6 ...(2)
Dividing equation (2) by equation (1), we get:
68/17 = (a r^6)/(a r^4)
4 = r^2
Taking the square root of both sides, we get:
r = ±2
Since the common ratio cannot be negative (otherwise the terms of the GP will alternate in sign), we take r = 2. Substituting this value of r into equation (1), we get:
17 = a (2^4)
17 = 16a
a = 17/16
Therefore, the first term of the GP is 17/16 and the common ratio is 2.