In an A.P. 17^th term is 7 more than its 10^th term. Find the common difference.

Given: t₁₇ = 7 + t₁₀ ……(1)

In t₁₇, n = 17

In t₁₀, n = 10

By using n^th term of an A.P. formula,

t_n = a + (n – 1)d

where n = no. of terms

a = first term

d = common difference

t_n = n^th term

Thus, on using formula in eq. (1) we get,

⇒ a + (17 – 1)d = 7 + (a + (10 – 1)d)

⇒ a + 16 d = 7 + (a + 9 d)

⇒ a + 16 d – a – 9 d = 7

⇒ 7 d = 7

Thus, common difference “d” = 1