if the sum of the first 4terms of an Ap is 40 and that of first 14 terms is 280find the sum of the first n term
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Step-by-step explanation:
Sn = sum of n terms of an A.P. = n/2 [ 2a + (n-1)d]
A/Q
S₄ = 40 = 4/2 [2a + 3d] = 2a + 3d = 20 ...........(1)
and
S₁₄ = 280 = 14/2 [2a + 13d] = 2a + 13d = 40 .........(2)
solving (1) and (2)
gives a = 7 and d= 2
so Sn = n/2[ 2(7) + (n-1)2] = 7n + n² - n = n² + 6n
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