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Question

The 4th and 10th terms of an AP are 13 and 25 respectively. Find the first term and the common difference of the AP. Also, find its 17th term.

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Solution

We have;
T4 = a + (n - 1)d
⇒ a + 3d = 13 ...(1)

​T10 = a + (n - 1)d
⇒ a + 9d = 25 ...(2)
On solving (1) and (2), we get:
a = 7 and d = 2

Thus, we have the following:
(i) First term = 7
(ii) Common difference = 2
(iii) T17 = a + (n - 1)d = a + 16d = ​7 + 16 ⨯ 2 = 39

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