Please help - Arithmetic progression

[Anonymous No.7276627]

I've been struggling for a long time with the following problem. Any help would be great and if possible could you show me how you got to the solution?

There are five numbers in an arithmetic sequence. Their sum is 25. The sum of their squares is 285. Find the five numbers.

[Anonymous No.7276637]

>>7276627
Write an equation for each statement:

let n be the first integer in the arithmetic sequence, let a be the interval of the arithmetic sequence

n + (n+a) + (n+2a) + (n+3a) + (n+4a) = 25
5n + 10a = 25

n^2 + (n+a)^2 + (a+2n)^2 + (n+3a)^2 + (n+4a)^2 = 285

^I'll leave this one for you to do algebraically on your own since its the only completely nontrivial part

Then you will have two equations in two variables, which you should be able to solve.

[Anonymous No.7276649]

>>7276637
Thanks for you r reply

I got n+2d = 5, and
n^2 + 4na + 6a^2 = 57

Do you know how I can proceed with this?

[Anonymous No.7276668]

The numbers are -3, 1, 5, 9, 13

[Anonymous No.7276691]

>>7276668
thanks, i got the answer from reddit cos a guy actually helped me understand how he got the solution rather than just give the answer. well done though, have a virtual trophy.