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Question
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Solution
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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