Question

if the 6th term of an arithmetic sequence is 48, and the sum of the first 6 term is 300, what is the first term and the constant difference?
Pls help as I have never learn this before,need some example to start with.thank you

Answer 1

You have to know the formulas for the general term and the sum of n terms of an arithmetic sequence

term6 = a + 5d = 48

sum6 = (6/2)(2a + 5d) = 300
3(2a + 5d) = 300
2a + 5d = 100
subtract the two two equations:
a = 52
back in a+5d = 48
52+5d = 48
5d = -4
d = -4/5

so the first term is 52
and the constant difference is -4/5 or -.8