Solution:
We have been asked to find the sum of the given geometric series.
The given Arithmetic series is
[tex] 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5) [/tex]
As we know the sum of the Arithmetic series is given by
[tex] 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]\\
[/tex]
[tex] \\
S_8=4*6.1=24.4\\ [/tex]
Hence Required Sum=24.4
