Question

find the sum all odd number between 100and150in a.p​

Answer 1

Answer:

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.

Answer 2

The odd numbers between 100 & 150 are

101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,147,149

total numbers = 25

average = sum of numbers/ total number

average =( 101+103+105.......+149) / 25

average= 3024/25

average = 120.96

ORIGINAL ANSWER By priya

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