Question

(iv) Find the sum of all numbers from 150 to 200 which are divisible by 8.
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Answer 1

Step-by-step explanation:

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Answer 2

The sum of all the numbers between 150 and 200 that are divisible by 8 is 1232 .

Given:

All numbers between 150 and 200

To find:

Sum of all numbers between 150 and 200 that are divisible by 8

Solution:

All the numbers between 150 and 200 that are divisible by 8 forms as Arithmetic progression whose first number is 152 and the last number is 200.

Let there are n numbers in the AP.

Given first term (a) = 152

last term (l) = 200

Common difference (d) = 8

Now we know that:

Last term = a + ( n - 1) d

or, 200 = 152 + (n-1)8

or, 48 / 8 = n-1

or, 6 +1 = n

or, n = 7

Therefore there are 7 numbers in the AP

Now sum of n numbers in an AP is given by

S = n / 2 (a + l )

or, S = 7 / 2 × (200+152)

or, S = 1232 .

Therefore the sum of all the numbers is 1232 .

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