Question

The sum of the first three terms of an arithmetic sequence is 108, and the sum of the next three terms is 183. what is the value of the 11th term

Answer 1

The key is to find the first term a(1) and the difference d.

in an arithmetic sequence, the nth term is the first term +(n-1)d
the firs three terms: a(1), a(1)+d, a(1)+2d
the next three terms: a(1)+3d, a(1)+4d, a(1)+5d,
a(1) + a(1)+d +a(1)+2d=108
a(1)+3d + a(1)+4d + a(1)+5d=183

subtract the first equation from the second equation: 9d=75, d=75/9=25/3
Plug d=25/3 in the first equation to find a(1): a(1)=83/3

the 11th term is: a(1)+(25/3)(11-1)=83/3 +250/3=111

Please double check my calculation. <span />