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प्रश्न
If the sum of first n terms of an AP is n2, then find its 10th term.
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उत्तर
We know sum of n terms of an AP is
Sn = n2
For n = 1, S1 = (1)2 = 1
So, a1 = 1
For n = 2, S2 = (2)2 = 4
For n = 3, S3 = (3)2 = 9
S2 - S1 = a2
⇒ a2 = 4 - 1 = 3
So, d = a2 - a1 = 3 - 1 = 2
We knopw nth term of an AP is
an = a + (n-1)d
For n = 10
a10 = 1+ (10 - 1)2
⇒ a10 = 1+ 9 × 2
⇒ a10 = 19
Thus, the 10th term of the AP is 19.
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