Question

Find the sum of all multiples of 7 greater than 100 and less than 400.​

Answer 1

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Answer 2

Given:

multiples of 7 greater than 100 and less than 400

To find:

Sum of all the multiples

Solution:

We have given the numbers from 100 to 400

but here we have to consider the terms which are the multiple of 7 only

and the terms are given by:

105, 112, 119,...............................399

So this is the arithmetic progression:

whose

• first term is -> a= 105
• Common difference -> d = 112-105 = 7
• Last term is 399

so the number of the terms can be given by:

aₙ = a+(n-1)d

• 399 = 105 +(n-1)7
• 294 = (n-1)7
• (n-1) = 294/7
• (n-1) = 42
• n= 42+1
• n = 43

So the sum of the trems of the AP is given by:

• Sₙ = n/2[2a+(n-1)d]
• S₄₃ = 43/2[2.105+(43-1)7]
• S₄₃ = 43/2[210+42×7]
• S₄₃ = 43/2[210+294]
• S₄₃ = 43/2[504]
• S₄₃ = 43×252
• S₄₃ = 10836

Hence, Sum of all the multiples is 10836