Sum of all two digit odd numbers is
Answers
step-1: first of all find the no. of two digit odd positive numbers (n) to be added by using the formula: tn= a + (n -1)d
where tn=lartgest two digit odd number.
a= smallest two digit odd number
d=common difference between two consecutive odd numbers
n=total no. of two digit odd numbers
step-2: now after finding the no. of two digit odd positive numbers present in the number system go for finding their sum (S) by using following formula:
S=(n/2)[2a+(n -1)d]
That’s it. ‘S’ is your answer.
Now finding the sum of two digit odd numbers by following above steps:
Two digit odd positive numbers are 11,13,15,17...........99 are in A.P.
Here a = 11 and d = 2, tn= 99, n = ?
Sum of the n terms = (n/2)[2a+(n -1)d]
But tn= a + (n -1)d
⇒ 99 = 11+ (n-1)2
⇒ 99 -11 = (n-1)2
⇒ 88/2 = (n-1)
∴ n = 45.
substitute n = 45 in sum of the n terms we obtain
⇒ S = (45/2)(2×11 + (45 -1)2)
⇒ S =(45/2)(110)
⇒S= 45×55.
⇒ S= 2475.
∴ sum of all two digit odd positive numbers = 2475.
Step-by-step explanation:
sum of all two digit odd no. is even
ex:
17+19=36