Question

Find the sum of first 100 natural multiple of 3

Answer 1

AnswEr:-

❀ Your Answer Is 15150.

ExplanaTion:-

To Find:-

• The sim of first 100 natural numbers which are multiple of 3.

Formula Used:-

$\tt\longrightarrow \bf{ S_n = \dfrac{n}{2} (a_1 + a_n).}$

Where,

• n = Numbers of terms.

• $\tt S_n$ = Sum of n terms.

• $\tt a_1 \:\: And \:\: a_n$ = First term and $\tt n^{th}$ respectively.

So,

• So the first 100 natural numbers which are multiple of 3 are:-

↦ 3, 6, 9........300.

(as 3 × 100 = 300).

Here we can see that the series is increasing with same difference which is 3. So we can say that these numbers are in AP.

Where,

• n = 100.

• Common Difference (d) = 3.

• $\tt a_1$ = 3.

• $\tt a_n \:\: i.e. \:\: 100^{th}\:\: term = 300$

Therefore

Sum of these terms:-

$\tt = \dfrac{n}{2} (a_1 + a_n). \\ \\ \tt = \cancel\frac{100}{2} (3 + 300). \\ \\ \tt = 50(303). \\ \\ {\boxed{\underline{\bf{= 15150.}}}}$

Therefore sum of first 100 natural numbers which are multiple of 3 is 15150.