Arithmetic sequences / partial sums

Question

I am given $a_5=8$ and $a_8=17$

I am asked to calculate the fourth partial sum but have no idea how.

Answer 1

enedil and Dr. Sonnhard Graubner have told you what an "arithmetic sequence" is. (If you didn't already know that, where did you get this question?)

Let "a" be the first number in the sequence and "b" be the "common difference. Then the second term is a+ b, the third term is (a+ b)+ b= a+ 2b, the fourth term is (a+ 2b)+ b= a+ 3b, the fifth term is (a+ 3b)+ b= a+ 4b= 8, the sixth term is (a+ 4b)+ b= a+ 5b, the seventh term is (a+ 5b)+ b= a+ 6b, and the eight term is (a+ 6b)+ b= a+ 7b= 17.

So you have a+ 4b= 8 and a+ 7b= 17. Solve those two equations for a and b (subtracting the first equation from the second is a good first step!). Then evaluate a+ 3b, the "fourth term" with those a and b.

Or just find b only then subtract b from the "fifth term", 8.