Question

Find sum of all odd nos. between 100 and 200.

Answer 1

Hii friend,

Odd numbers lying between 100 to 200 are:

101 , 103 , 105 , 107........199

AP= 101, 103 , 105,.....199

Here,

first term (a) = 101

Common difference (d) = 2

Tn = 199

a+(n-1) × d = 199

101 +(n-1) × 2 = 199

101 + 2n -2 = 199

2n = 199-99

2n = 100

n = 100/2 = 50

Sn= N/2 × [ 2a+ (n-1) × d]

S50 = 50/2 × [ 2 × 101 + (50-1) × 2]

=> 50/2 × [ 202 + 98]

=> 50/2 × 300

=> 25 × 300

=> 7500

Hence,

The sum of odd numbers between 100 to 200 is 7500.

HOPE IT WILL HELP YOU..... :-)

Answer 2

Answer:

101,103,105...........199

an = 199  a = 101  d= 2

an= a+ (n-1)d

199 = 101 +(n-1) 2

199-101 = (n-1)2

98/2  = n-1

49 +1 = n

so,  n= 50

sn = n/2 (a+l)

=  50/ 2 (101+199)

 = 25 x 300

 = 7500