Question

What is the sum of the finite arithmetic series? 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)

Answer 1

Solution:

We have been asked to find the sum of the given geometric series.

The given Arithmetic series is

$7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)$

As we know the sum of the Arithmetic series is given by

$S_n=\frac{n}{2}[2a+(n-1)d] \\ \\ \text{where a= first term, n=Total number of terms , d=Common diffrence}\\ \\ \text{Here we have}\\ \\ a=7.6, d=-1.3, n=8\\ \\ \text{Substitute the values in the above formula we get}\\ \\ S_8=\frac{8}{2}[2*7.6+(8-1)(-1.3)] \\ \\ S_8=4[15.2-9.1]$

$\\ S_8=4*6.1=24.4$

Hence Required Sum=24.4

Answer 2

The sum of this series is 24.4