Question

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

Answer 1

In an A.P., 17^th term is 7 more than its 10^th term.  ...(Given)

The formula for n^th term of an A.P. is t_n = a + (n − 1)d

The 10^th term can be written as,

t₁₀ = a + (10 − 1)d 

t₁₀ = a + 9d

The 17^th term can be written as,

t₁₇ = a + (17 − 1)d 

t₁₇ = a + 16d 

Now, according to the question,

t₁₇ = 7 + t₁₀

Substituting the value of t₁₇ and t₁₀ in the above equation,

∴ a + 16d = 7 + a + 9d

∴ 16d = 7 + 9d

∴ 16d − 9d = 7

∴ 7d = 7

∴ d = `7/7` = 1

Hence, the common difference of the given AP is 1.