If 17^th term of an A.P. exceeds its 10^th term by 7. Find the common difference.

We know that the n^th term of an arithmetic progression is given as:

a_n = a+(n−1)d

Let us substitute the values given in the question:

a₁₇ = a + (17−1)d

a₁₇ = a + 16d

Also,

a₁₀ = a + 9d

According to the given condition,

a₁₇ − a₁₀ = 7

Therefore,

(a + 16d) − (a + 9d) = 7

7d = 7

d = 1

Therefore, the common difference is 1.