If the sum of first four terms of an AP is 40 and that of first 14 ter

1.	If the sum of first four terms of an AP is 40 and that of first 14 terms is 280.Find the sum of its first n terms.
Answer» 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

If the sum of first four terms of an AP is 40 and that of first 14 terms is 280.Find the sum of its first n terms.

Answer»

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