SOLUTION: The fifth term of an Arithmetic progression is 24 and the sum of the first five terms is 80, find the first term common difference and the sum of the first fifteen terms of the A.P

Algebra ->  Sequences-and-series -> SOLUTION: The fifth term of an Arithmetic progression is 24 and the sum of the first five terms is 80, find the first term common difference and the sum of the first fifteen terms of the A.P      Log On


   

Question 972097: The fifth term of an Arithmetic progression is 24 and the sum of the first five terms is 80, find the first term common difference and the sum of the first fifteen terms of the A.P
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General term A%5Bn%5D=A%5B1%5D%2B%28n-1%29d.
A%5B5%5D=A%5B1%5D%2B%285-1%29%2Ad=24, fifth term.

%285%2F2%29%28A%5B1%5D%2BA%5Bn%5D%29=80---- a strong clue for the last part of the question.
%285%2F2%29%28A%5B1%5D%2B24%29=80
A%5B1%5D%2B24=80%282%2F5%29
A%5B1%5D=-24%2B32
highlight%28A%5B1%5D=8%29

Again from the general term used for the formula for the fifth term,
A%5B1%5D%2B4%2Ad=24
4d=24-A%5B1%5D
4d=24-8
4d=16
highlight%28d=4%29