Question

find the sum of all odd integers between 100 and 200​

Answer 1

all odd integers between 100 and 200 are 101,103,105........199

here,

a=101

d=2

tn=199

to find Sn

tn=a+(n-1)d

199=101+(n-1)2

199-101=(n-1)2

98=2n-2

98+2=2n

100=2n

n=50

Sn=n/2(a+tn)

Sn=50/2(101+199)

Sn=25(300)

Sn=7500

hence, the sum of all odd integers between 100 and 200 is 7500

hope this helps you.

:-)

Answer 2

TO FIND :- The sum of all odd integers between 100 and 200.

SOLUTION :-

This Question can be solved by using concept of Arithematic Progression.

GIVEN :-

First term (a) = 101

last term (l) = 199

common difference (d) = 2

${a}_{n} = a + (n - 1)d \\ \\ \\ \implies 199 = 101 + (n - 1)2 \\ \\ \\ \implies 98 = (n - 1)2 \\ \\ \\ \implies 49 = n - 1 \\ \\ \\ \implies \boxed{n = 50}$

Now, We will use sum formula of AP to find the sum :-

${s}_{n} = \frac{n}{2} (a + l) \\ \\ \\ = \frac{50}{2} (101 + 199) \\ \\ \\ = 25(300) \\ \\ \\ \implies \boxed{7500}$

THE SUM OF ALL ODD NUMBERS BETWEEN 101 and 199 is 7500.