The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

Sum of the first n term is given by (s_n) = [2a + (n-1) d]

The sum of first 7 terms S₇ = 49 → 7²

S₇ = [2×a+(7-1)d]

49 = [2a+6d]

49 = 7[a+3d]

7 = a + 3d ⇒ 1

The sum of first 17 terms S₁₇ = 289 → 17²

S₁₇ = [2×a+(17-1)d]

289 = [2a+16d]

289 = 17[a+8d]

17 = a + 8d ⇒ 2

By subtracting both the equations

17 – 7 = a + 8d – (a+3d)

10 = 5d

d =2

∴ common difference (d) = 2

Substituting‘d’ in equation 1

7 = a + 3d

7 = a + 3(2)

a = 1

∴ Sum of the first n term is given by (s_n) = [2a + (n-1) d]

= [2×1 + (n-1)2]

= n[ 1+ (n-1)]

= n²