Question

Find the sum of all odd integers between 10 and 110, which are divisible by 3.

Answer 1

hope it help you to find answer

Answer 2

Sum of all odd integers between 10 and 110, which are divisible by 3 is 960

Solution:

Consider the odd natural numbers between 10 and 110

15, 21, .............. , 105

This forms a arithmetic progression with common difference 6

Therefore, the number of terms:

l = a + (n - 1)d

Where,

l is the last term

a is first term

n is number of terms

d is common difference between terms

Therefore,

l = 105

a = 15

d = 6

Substituting we get,

$105 = 15 + (n - 1) \times 6\\\\105 = 15 + 6n - 6\\\\6n = 96\\\\n = 16$

Therefore, the sum will be:

$Sum = \frac{n}{2} \times (a + l)\\\\Sum = \frac{16}{2} \times (15 + 105)\\\\Sum = \frac{16}{2} \times 120 \\\\Sum = 960$

Thus, sum of all odd integers between 10 and 110, which are divisible by 3 is 960

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