Question

Find sum of all the odd number lying between 100 and 200

Answer 1

Odd number lying between 100 and 200 are

101, 103, 105, ........, 199 represent an AP whose first term a = 101,  common difference d = 2 and nth term = 199

So we know that

an = a+(n-1)d

⇒ 199 = 101 +(n-1)2

⇒ 98 = (n-1)2

⇒ n-1 = 49

⇒ n = 50

So in given AP number of term = 50

Now evaluate the sum of given AP

Sn = n/2 [a+an]

⇒ Sn = n(a+an)/2

⇒ Sn = 50(101+199)/2

⇒ Sn = 25×300

⇒ Sn = 7500

Answer 2

Answer:

refers to the attachment