The pth term of an A.P. is 1/7(2p-1). Find the sum of its first n terms.
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sum of its first n terms = n²/7 if The pth term of an A.P. is (2p- 1)/7
Step-by-step explanation:
Tp = (2p- 1)/7
T₁ = (2 * 1 - 1)/7 = (2 - 1)/7 = 1/7
T₂ = (2 *2 - 1)/7 = (4 - 1)/7 = 3/7
d = 3/7 - 1/7 = 2/7
a = First Term = 1/7
nth term = a + (n-1)d
= 1/7 + (n - 1)(2/7)
= (1 + 2n - 2)/7
= (2n - 1)/7
Sum of n terms = (n/2)(First term + nth term)
= (n/2)(1/7 + (2n - 1)/7)
= (n/2)(1 + 2n - 1)/7
= (n/2)(2n/7)
= n²/7
sum of its first n terms = n²/7
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