Question

The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.

Answer 1

an arithmetic sequence is of the form
\[ \large a_1\qquad\text{not given} \]
\[ \large a_2=a_1+d \]
\[ \large 9=a_3=a_2+d=a_1+2d \]
so
\[ \large 31=a_7=a_1+6d \]

Answer 2

u end up with
\[ \large 9=a_1+2d \]
\[ \large 31=a_1+6d \]
solve this system

Answer 3

r u there @katiebugg ?

Answer 4

sorry
yeahh was working on a prob thanks!!!