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Sequences & Series Worksheet

Algebra 2 Math · printable worksheet (PDF) with answer key · 15 problems · CCSS HSF.BF.A.2, HSA.SSE.B.4

A printable algebra 2 sequences & series practice worksheet with 15 problems and a complete, step-by-step answer key — formatted to print cleanly on standard paper. Included in the one-time $20 unlock for the full NudgeLearn library.

Sample problems

Show your work. Arithmetic: $a_{n} = a_{1} + (n - 1) d$ and $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ . Geometric: $a_{n} = a_{1} r^{n - 1}$ and $S_{n} = a_{1} \frac{1 - r ^{n}}{1 - r}$ . Infinite geometric ( $∣ r ∣ < 1$ ): $S = \frac{a _{1}}{1 - r}$ .

1. Find the $15$ th term of the arithmetic sequence with $a_{1} = 6$ and common difference $d = 4$ .
2. Find the $7$ th term of the geometric sequence with $a_{1} = 2$ and common ratio $r = 3$ .
3. Write an explicit formula for the $n$ th term of the arithmetic sequence $3, 10, 17, 24, \dots$
4. Write an explicit formula for the $n$ th term of the geometric sequence $4, 12, 36, 108, \dots$

Plus 11 more problems and a full answer key in the PDF.

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