IB Mathematics Applications & Interpretation Question Type 1: Finding the Sum to Infinity of a Given Sequence Exercises

Given that the sum to infinity of a geometric series is $20$ and its first term is $5$, find the common ratio $r$.

Calculate the sum to infinity.

Find the sum to infinity of the geometric sequence defined by $u_n=2\cdot (0.8{)}^{n-1}$.

Calculate the sum to infinity of the series $3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\dots$.

Determine the sum to infinity of the geometric sequence with first term $u_1=12$ and common ratio $r=\frac{3}{4}$.

Show that the infinite sum of the sequence $7,\frac{7}{4},\frac{7}{16},\dots$ equals $\frac{28}{3}$.

Find the sum to infinity of the sequence $8,-4,2,-1,\dots$.

A geometric series has common ratio $r=\frac{2}{5}$ and sum to infinity $15$. Find its first term.

Calculate the sum to infinity of the geometric sequence with first term $u_1=5$ and common ratio $r=\frac{1}{3}$.

Given that $\sum _{n=1}^{\infty }{u}_n=30$ and the common ratio $r$ satisfies $\frac{1}{r}+1=5$, find $u_1$.