Question

The sum of all the numbers between 1 and 200 which are multiples of 4

Answer 1

The sum of all multiples of 4 is "4900".

Step-by-step explanation:

The number between 1 to 200 mutiple of 4 are:

4,8, 12,........, 196

The above sequence are in A.P.

Here, first term(a) = 4, common difference(d) = 8 - 4 = 4 and last term (l) = 196

Let n be the number of terms.

196 = 4 + (n - 1) × 4

⇒  (n - 1) × 4 = 196 - 4 = 192

⇒  (n - 1)  = 48

∴ n = 48 + 1 =  49

∴ $S_{n}$ = $\dfrac{49}{2}$ × {2 × 4 + 48 × 4}

= $\dfrac{49}{2}$ ×  {8 + 192}

= $\dfrac{49}{2}$ ×  200

= 4900

Hence, the sum of all multiples of 4 is "4900".

Answer 2

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