Problem with arithmetic series

Question

Define the arithmetic series if $A_3 + A_7 = 28$, $S_{10} = 155$.

We have this for homework, I browsed the internet and I tried to find a formula or the way but there is nowhere I can find anything.

Can someone at least guide me through the first steps, so then I will continue with the rest ?

Thank you!

Answer 1

Assuming $A_r$ is the $r$th term and $d$ be the common difference

$\implies A_r=A_1+(r-1)d$

$\implies28=A_3+A_7\iff2A_1+8d=28$

and $155=S_{10}=\dfrac{10}2[2A_1+(10-1)d]\iff2A_1+9d=\dfrac{155}5$

Can you determine $A_1,d$ from here?

Answer 2

Note: I am assuming that the sequence starts with $A_1$ (it makes the numbers come out nicer), rather than $A_0$.

Hints:

(1) $A_5$ is the average of $A_3$ and $A_7$.

(2) $A_1+A_{10}=A_2+A_9=...$. So $5(A_5+A_6)=S_{10}$.