Question

if the sum of the first 7 term of an ap is 4g and that of 17 terms is 289 find the sum of the first n terms​

Answer 1

Answer:

n²

Step-by-step explanation:

I think the "4g" was meant to be "49".  Let's proceed with that.

Let a be the first term and d the common difference.

The sum of the first n terms is na + [n(n-1)/2]d.

Putting n = 7:

7a + 7×3d = 49   =>   a + 3d = 7      ... (1)

Putting n = 17:

17a + 17×8d = 289   =>   a + 8d = 17      ... (2)

Subtracting equation (1) from equation (2):

5d = 10   =>   d = 2

Then from equaiton (1):

a = 7 - 3d = 7 - 6 = 1

Therefore, the sum of  the first n terms is

na + [n(n-1)/2]d

= n + n(n-1)

= n + n² - n

= n²

Answer 2

Answer:

Step-by-step explanation: