Question

Question 2 (i)
Find the sums given below
(i) $7+10\frac{1}{2}+14+\dots \dots +84$

Answer 1

(i)
For this A.P.,
a = 7
$a_n=84$
$d=a_2-a_1=10\frac{1}{2}-7=\frac{21}{2}-7=\frac{7}{2}$
Let 84 be the $n^{th}$ term of this A.P.
$a_n=a+(n-1)d84=7+(n-1)\times \frac{7}{2}77=(n-1)\times \frac{7}{2}22=n-1n=23Weknowthat,S_n=\frac{n}{2}(a+a_n)S_{23}=\frac{23}{2}(7+84)=(23\times \frac{91}{2})=\frac{2093}{2}=1046\frac{1}{2}$