Question

In an AP the first term is 8, nth term is 33 and the sum to n terms is 123. Find the number of terms and common difference.

Answer 1

Hi,

number of terms =n=6

common difference=r=5

(why r ? In french, the common difference is called "la raison"

Explanation:

a=first term=8

nth term is 33 :

`a+(n-1)*r=33 \Longrightarrow\ r(n-1)=25\\`

`r=(25)/(n-1)`

The sum to n terms is 123:

`a_1+(a_1+r)+(a_1+2r)+...+a_1*(n-1)*r=123\\\\n*a_1+r*(n*(n-1))/(2) =123\\\\16*n+r*n*(n-1)=246\\\\16*n+(25*n*(n-1))/(n-1) =246\\\\41*n=246\\\\n=6\\\\r=(25)/(5) =5\\`