In an A.P. 17th term is 7 more than its 10th 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 = number 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
⇒ d = 7/7 = 1
Thus, common difference “d” = 1