Question

Find the sum of the numbers between 200 and 500.Which is the multiple of 7

Answer 1

Answer:

1. 500 + 200 = 700
2. 700 multiple of 7 = 1400

Answer 2

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QUESTION :

Find the sum of the numbers between 200 and 500 which is the multiple of 7.

SOLUTION :

Given that,

Numbers in between 200 & 500 which is a multiple of 7 are : 203,210,217.....497

Therefore,the AP series is

→ 203,210,217....497

• a1 = 203 & a2 = 210

Common difference (d) = a2 - a1

= 210 - 203

= 7

Therefore,the common difference (d) is 7.

Now we have

• a = 203, d = 7, an = 497, n = ?

➢ To find number of terms...

⟹ an = a + (n - 1)d

• substitute the values to get no.of terms

➡ 497 = 203 + (n - 1)7

➡ 497 = 203 + 7n - 7

➡ 497 = 196 + 7n

➡ 7n = 497 - 196

➡ 7n = 301

➡ n = 301/7

➡ n = 43

Therefore,the no.of terms are 43

➢To find the sum of the terms, we need to use the formula

⟹ Sn = n/2 [ 2a + (n - 1)d ]

• Substitute the values to get sum of terms.

➡ S43 = 43/2 [ 2(203) + (43 - 1)7 ]

➡ S43 = 43/2 [ 406 + (42)7 ]

➡ S43 = 43/2 [ 406 + 294 ]

➡ S43 = 43/2 [ 700 ]

➡ S43 = (43 × 700)/2

➡ S43 = 43 × 350

➡ S43 = 15050

Therefore,the sum of the numbers between 200 and 500 which is the multiple of 7 is 15050.

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