Question

Find the sum of all odd numbers between 30 to 120 using series method

Answer 1

Answer:

let a & d be the first term and the common difference respectively

the AP will be as follows :-

31 , 33 , 35 ,.............................119

a =  31

d = 33 - 31 = 2

first to find the sum we must know the total number of terms in it

thus, $t_{n} = a + (n - 1)d$

$119 =31 + (n - 1)2\\\\88 = (n - 1)2\\\\n - 1 = 44\\\\n = 45$

let l be the last term of the AP i.e 119

$S_{45} = \frac{n}{2}[a + l]\\ \\S_{45} = \frac{45}{2}[31 + 119]\\\\S_{45} = \frac{45}{2}[150]\\\\S_{45} = 45 * 75\\\\S_{45} = 3375$