SOLUTION: The first term of an arithmetic progression is -12,and the last term is 40. If the sum of the progression is 196,determine the: (i)the number of terms (ii)common difference

Algebra ->  Finite-and-infinite-sets -> SOLUTION: The first term of an arithmetic progression is -12,and the last term is 40. If the sum of the progression is 196,determine the: (i)the number of terms (ii)common difference       Log On


   

Question 1040989: The first term of an arithmetic progression is -12,and the last term is 40. If the sum of the progression is 196,determine the:
(i)the number of terms
(ii)common difference
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
From the sum,
S%5Bn%5D=%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29
196=%28n%2F2%29%28-12%2B40%29
392=n%2828%29
n=14
.
.
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
40=-12%2B%2814-1%29d
13d=52
d=4