Question

The 8th term of an AP is 11 and the 15th term is 21. find the sum of the first 8 terms

Answer 1

For the n-th term of AP we have

$$a_n=a_1+(n-1)d$$

Therefore

$$a_8=a_1+7d=11$$

$$a_{15}=a_1+14d=21$$

We obtain

$$a_1=1,\quad d=10/7$$

The sum of the first 8 terms

$$S_8=\frac{a_1+a_8}{2}\times 8=\frac{1+11}{2}\times 8=48$$