Infinite Sequences & Series

The next term of the sequence $2,4,6,8,...$ is ...

The next term of the sequence $3,6,12,24,...$ is ...

The common difference of the sequence $5,9,13,17,...$ is ...

The common ratio of the sequence $2,6,18,54,...$ is ...

Given $U_n=2n+1$. The value of $U_5$ is ...

The sum $1+2+3+4+5$ is ...

The sum to infinity of a geometric series with first term 8 and ratio $\frac{1}{2}$ is ...

The sum to infinity of a geometric series with first term 12 and ratio $\frac{1}{3}$ is ...

An arithmetic sequence has first term 3 and common difference 4. The 10th term is ...

A geometric sequence has first term 2 and ratio 3. The 5th term is ...

An infinite geometric series converges (has a sum) if its ratio is ...

The sum of the series $1+\frac{1}{2}+\frac{1}{4}+\cdots$ is ...

The sum of the first 10 odd numbers $1+3+5+\cdots$ is ...

A geometric sequence has $U_3=12$ and $U_5=48$. Its positive ratio is ...

An infinite geometric series has $S_{\infty }=4$ and first term $a=3$. Its ratio is ...

The fraction form of the repeating decimal $\mathrm{0.333...}$ is ...

The fraction form of the repeating decimal $\mathrm{0.121212...}$ is ...

The sum of the series $2-1+\frac{1}{2}-\frac{1}{4}+\cdots$ is ...

A ball is dropped from a height of 8 m. On each bounce it reaches $\frac{3}{4}$ of the previous height. The total distance traveled by the ball until it stops is ...

An infinite geometric series has first term 6 and sum to infinity 9. Its ratio is ...