Question

Find the indicated sum of each series: 2 + 4 + 8 + …; S₁₅ ​

Answer 1

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

=

2

n

[2a+(n−1)d]

S

15

=

2

15

[2×2+(15−1)2]

S

15

=7.5[4+28]

S

15

=240