1.

Find the sum of all numbers from 150 to 200 which are divisible by 8. ​

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Answer:

Sum of all numbers from 150 to 200 which are divisible by 8 is 1232.

Step-by-step EXPLANATION:

We must first find numbers which are divisible by 8 between 150 to 200

They are:-

152, 160, 168,...., 192, 200

Now, If we observe this sequence they form an A.P.

Here,

a = 152

d = 160 - 152 = 8

and the last term is 200

l (last term) = 200

So,

a(nth) = 200

Now, we KNOW that,

a(nth) = a + (N - 1)d

200 = 152 + (n - 1)8

200 - 152 = 8(n - 1)

48 = 8(n - 1)

n - 1 = 48/8

n - 1 = 6

n = 6 + 1

n = 7

Hence,

There are 7 terms in this A.P

We know that,

Sn = (n/2)[a + l]

where n is number of terms, a is first term and l is last term.

So,

Sn = (7/2)(152 + 200)

Sn = (7/2)(352)

Sn = 7 × 176

Sn = 1232

Hence,

Sum of all numbers from 150 to 200 which are divisible by 8 is 1232.

Hope it helped and believing you understood it....All the best



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