Sum of first five multiples of 3 is. . . - Vidyadip

MCQ

Sum of first five multiples of 3 is. . .

✓
45
B
55
C
15
D
75

✓

Answer

Correct option: A.

45

(A) 45
First five multiples of 3 are
$3,6,9,12,15$
First term $a =3$
Second term $t_1=6$
Third term $t_2=9$
Common difference $d=t_2-t_1=9-6=3$
Thus, By using sum of $n^{\text {th }}$ term of an A.P. we will find it's sum
$S_n=\frac{n}{2}[2 a+(n-1) d]$
Where, $n=$ no. of terms
a = first term
d = common difference
S_n = sum of n terms
We need to find S₅$\begin{array}{l}
\Rightarrow S_5=\frac{5}{2}[2 \times 3+(5-1) \times 3] \\
\Rightarrow S_5=\frac{5}{2}[6+4 \times 3] \\
\Rightarrow S_5=\frac{5}{2}[6+12] \\
\Rightarrow S_5=\frac{5}{2} \times 18=5 \times 9=45
\end{array}$
Thus, correct answer is (A)

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