Question

find the sum of all multiples of 4 from to 200​

Answer 1

Answer:

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}S

n

= \dfrac{49}{2}

2

49

× {2 × 4 + 48 × 4}

= \dfrac{49}{2}

2

49

× {8 + 192}

= \dfrac{49}{2}

2

49

× 200

= 4900

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

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