IB Mathematics Applications & Interpretation Question Type 6: Finding Common Ratio or Sum of First n Terms Given the Values of Other Sums Exercises

Given a geometric series with $S_4=15$ and $S_6=63$, find the first term and common ratio.

The sum of the first $n$ terms of a series is given by $S_n=n^2+5n$. Find $n$ if $S_n=84$.

A geometric series has common ratio $r=2$ and sum of the first 4 terms $S_4=15$. Find the first term and $S_6$.

A geometric series has sum to infinity $S_{\infty }=16$ and sum of the first two terms $S_2=12$. Find the possible values of the first term $a$ and the common ratio $r$.

Given an arithmetic series with $S_4=22$ and $S_7=70$, find the first term and common difference.

The sum of the first $n$ terms of an arithmetic series is given by $$S_n=6n-n^2.$$ Find its first term and common difference.

The sum of the first $n$ terms of a series is given by $$S_n=3n^2+n.$$ Assuming the series is arithmetic, find its first term and common difference.

Given a geometric series with positive terms such that $S_2=5$ and $S_6=105$, find the first term and common ratio.

Given an arithmetic series with $S_8=208$ and $S_{12}=456$, find the first term and common difference.

Given an arithmetic series with $S_4=26$ and $S_{10}=155$, find $S_{15}$.

Given a geometric series with $S_3=7$ and $S_5=31$, find the common ratio and the sum of the first 7 terms.

Given an arithmetic series with $S_7=77$ and $S_{15}=345$, find $S_8$.