Question

The sum of the first 7 terms of an AP is 49 and the sum of its first 17 term is 289. Find the sum of its first n terms.

Answer 1

Let a be the first term and d be the common difference of the given AP. Then, we have:

However, S₇ = 49 and S₁₇ = 289

Now, 7(a + 3d) = 49

\(\Rightarrow\) a + 3d = 7 .......(i)

Also, 17[a + 8d] = 289

\(\Rightarrow\) a + 8d = 17 .......(ii)

Subtracting (i) from (ii), we get:

5d = 10

\(\Rightarrow\) d = 2

Putting d = 2 (in), we get

a + 6 = 7

\(\Rightarrow\) a = 1

Thus, a = 1 and d = 2