#### Question

Find the sums given below : 7 + `10 1/2` + 14 + .................. +84

#### Solution

For this A.P.,

*a* = 7

*l* = 84

*d* = *a*_{2} − *a*_{1} = `10 1/2 - 7 = 21/2 - 7 = 7/2`

Let 84 be the nth term of this A.P.

l = a (n - 1)d

`84 = 7 + (n - 1) × 7/2`

77 = (n - 1) × 7/2

22 = n − 1

n = 23

We know that,

`S_n = n/2 (a + l)`

`S_n = 23/2 [7 + 84]`

`= (23×91)/2 = 2093/2`

`= 1046 1/2`

Is there an error in this question or solution?

Solution Find the sums given below : 7 + `10 1/2` + 14 + .................. +84 Concept: Sum of First n Terms of an AP.