Question

In algebraic sewuence the first term is 6 and sum.Of first n numbers is 66 what is the commmon difference

Answer 1

Answer:

if n = 2 then d = 54

if n = 3 then d = 16

and so on

Step-by-step explanation:

In given AP

a = First Term = 6

d = common difference = to be find

n = Number Of Terms

nth Term = a + (n-1)d

Sum of n terms = (n/2)(a + nth Term)

=> (n/2)(6 + 6 + (n-1)d) = 66

=> n ( 12 + (n-1)d) = 132

=>  12n + dn(n-1) = 132

value of d depend upon n

Lets say n =2

then

12 × 2  + d×2(2-1) = 132

=> 2d = 108

=> d = 54

Let say n = 3

=> 12×3 + d×3×(3-1) = 132

=> 6d = 96

=> d = 16

and so on