[Math] Arithmetic sequence: finding sum of n term with two terms

Question

I am completely stuck on a question. I've done it 4 times, each times got different result, but never correct.

The third term of an arithmetic progression is 71 and the seventh term is 55. Find the sum of the first 45 terms.

Any ideas? Thanks

Answer 1

$a+2d=71...1 $ while $a+6d=55$ solving you get $d=-4,a=79$ thus now sum =$\frac{45}{2}(158+(44)(-4))=-405$ thus its solved