Question

Find the sum of the following AP : $2,4,6,8,......(15$ terms).

• A. $210$
• B. $220$
• C. $230$
• D. $240$

Answer 1

Answer: (D)

$240$

First term of the given arithmetic series = 2
Second term of the given arithmetic series = 4
Third term of the given arithmetic series = 6
Fourth term of the given arithmetic series = 8
Now, Second term - First term = 4 - 2 = 2
Third term - Second term = 6 - 4 = 2
Therefore, common difference of the given arithmetic series is 2.
The number of terms of the given A. P. series (n) = 15
We know that the sum of first n terms of the Arithmetic Progress, whose first term = a and common difference = d is
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$S_{15}=\frac{15}{2}[2\times 2+(15-1\left)2\right]$
$S_{15}=7.5[4+28]$
$S_{15}=240$