Question

In an arithmetic progression, if the kth term is 5k+1, then the sum of first 100 terms is

A. 50(507)
B. 51(506)
C. 50(506)
D. 51(507)
E. 52(506)

Answer 1

The sum of the first 100 terms of an arithmetic progression with the kth term equal to 5k+1 is found by using the sum formula for an AP. The common difference is 5, and the first term is 6. The sum of the first 100 terms is 50(507). So the correct answer is option 1.

Step-by-step explanation:

The kth term of an arithmetic progression (AP) is given as 5k+1. To find the sum of the first 100 terms, we can use the formula for the sum of the first n terms of an AP, which is Sn = n/2(2a + (n-1)d), where a is the first term, n is the number of terms, and d is the common difference. The first term a1 = 5(1)+1 = 6 and the second term a2 = 5(2)+1 = 11, so the common difference d = a2 - a1 = 11 - 6 = 5. Applying this to the sum formula for n = 100 terms:

S100 = 100/2(2(6) + (100-1)(5)) = 50(12 + 495) = 50(507).

Therefore, the sum of the first 100 terms of this AP is 50(507).