Q13 of 176 Page 8

Find the sum : 25 + 28 + 31 +… + 100

Here, a = 25, d = 28 – 25 = 3 and a_n = 100

We know that,

a_n = a + (n – 1)d

⇒ 100 = 25 + (n – 1)3

⇒ 75 = (n – 1)3

⇒ 25 = n – 1

⇒ 26 = n

Now,

⇒ S₂₆ = 13[50 + 25 × 3]

⇒ S₂₆ = 13[50 + 75]

⇒ S₂₆ = 13 × 125

⇒ S₂₆ = 1625

If the sum of n terms of an A.P. is pn + qn², where p and q are constants, find the common difference.

If the sum of n terms of an A.P. is nP + 1/2 n( n —1)Q , where P and Q are constants, find the common difference of the A.P.

Which term of the A.P. 4, 9, 14, ... is 89? Also, find the sum 4 + 9 + 14 + + 89.

Solve for x

1 + 6+11 + 16 +...+x= 148