Question

Explain the terms in the formula sn= n/2 2a+(n-1)d

Answer 1

Answer:

The sum of nth terms of an AP with first term a and common difference d is Sn=n2(2a+(n-1)d) The sum of first 6 terms of an arithmetic progression is 42. The ratio of its 10th term to its 30th term is 1:3.

Answer 2

In the given formula,

Sn = Sum of n terms

n = Total number of terms

a = The first term

d = common difference

1. The given formula is $S_{n} = \frac{n}{2} ( 2a + (n-1)d)$. It is used to find the sum of n terms in an arithmetic progression.

2. For example, A.P. = 2,4,6,8,10,12

    n = 6, a = 2,

    d = 6-4 = 2      (The difference between two consecutive terms)

    Therefore, the sum of 6 terms will be

      $S_{n} = \frac{n}{2} ( 2a + (n-1)d)$

            $= \frac{6}{2} (2*2 + (6-1)2)$

            $= 3(4 + 5*2)$

            $= 3(4 + 10)$

            $= 42$

Hence, the sum of 6 terms is equal to 42.