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प्रश्न
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
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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:
T 10 = 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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