Question

find the first ten terms of the series 1-3/2+9/4

Answer 1

\(\Large \color{midnightblue}{\rightarrow ({- 3 \over 2})^{n} }\)

This is the formula :)

Answer 2

this is an alternating geometric sequence the ratio of the terms will give the common ratio

use
\[\frac{T _{2}}{T _{1}}=\frac{T _{3}}{T _{2}} = ...\]

find the common ratio and then its previous term multiplied by the common ratio....

\[(\frac{-3}{2})^n\] works for n = 0, 1, 2, 3, .......

or it could be written

\[(\frac{-3}{2})^{n-1}\]

where n = 1, 2, 3, 4, 5,....