Question

1) Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10..

0.005
0.321
0.964
10.714

Answer 1

\[\large 25\sum_{n=2}^{n=10}0.3^{(n+1)}\]
The 25 can be taken outside the sigma sign, the reason being it is a common factor of the 9 terms in the summation.
We have a geometric sequence, with r = 0.3, n = 9 and the first term being 0.3^3 = 0.027.
The sum of the 9 terms of the sequence is given by:
\[\large S _{9}=\frac{0.027(1-0.3^{9})}{1-0.3}\]
When you have calculated the sum of the geometric sequence, multiply by 25 to find the required summation.