(a) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:
number of terms in the series;
(b) The first term of an Arithmetic Progression is -8, the last term is 52 and the sum of terms is 286. Find the:
common difference.
Explanation
(a) a=8;l=52;n=?
\(S_n=\frac{n}{2}(a+l)=286\)
\(=\frac{n}{2}(-8+52)=286\)
\(=\frac{n}{2}(44)=286\)
=22n=286
\(∴n=\frac{286}{22}=13\)
(b) l = a + (n - 1)d = 52
= -8 + (13 - 1)d = 52
= -8 + 12d = 52
= 12d = 52 + 8
= 12d = 60
\(∴d=\frac{60}{12}=5\)