Question:

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

Updated On: Nov 3, 2023
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Solution and Explanation

We know that, For an A.P.,
an=a+(n1)da_n = a + (n − 1) d
a17=a+(171)da_{17} = a + (17 − 1) d
a17=a+16da_{17} = a + 16d       ……. (i)
Similarly,
a10=a+(101)da_{10} = a + (10− 1) d
a10=a+9da_{10}= a + 9d       ……. (ii)
It is given that,
a17a10=7a_{17} − a_{10} = 7
(a+16d)(a+9d)=7(a + 16d) − (a + 9d) = 7
7d=77d = 7
d=1d = 1

Therefore, the common difference is 1.

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