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प्रश्न
If the 10th term of an A.P. is 52 and the 17th term is 20 more than the 13th term, find the A.P.
उत्तर
In the given AP, let the first term be a and the common difference be d.
Then, Tn = a + (n − 1)d
Now, we have:
T10 = a + (10 − 1)d
⇒ a + 9d = 52 ...(1)
T13 = a + (13 − 1)d = a + 12d ...(2)
T17 = a + (17 − 1)d = a + 16d ...(3)
But, it is given that T17 = 20 + T13
i.e., a + 16d = 20 + a + 12d
⇒ 4d = 20
⇒ d = 5
On substituting d = 5 in (1), we get:
a + 9 ⨯ 5 = 52
⇒ a = 7
Thus, a = 7 and d = 5
∴ The terms of the AP are 7, 12, 17, 22,...
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