Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

The arithmetic sequence 9, 9.5, 10, 10.5, … ends with the term 20. How many terms n does it have?

a₁ = 9d = 0.5aₙ = 20

n =

2.Easy

Find the sum S₂₂ of the first 22 terms of the arithmetic sequence 4, 9, 14, 19, …

a₁ = 4d = 5n = 22

S₂₂ =

3.Medium

Apply the root test to Σ_k=1^∞ ((5k + 3)/(3k + 5))ᵏ. Find L = lim |a_k|^1/k.

a_k = ((5k + 3)/(3k + 5))ᵏ

L =

4.Medium

Find the sum S = Σ_k=1^∞ 3/(k(k + 4)).

a_k = 3/(k(k + 4))

S =

5.Hard

Find the coefficient c₃ of (x − 3)³ in the Taylor series of f(x) = 1/x about a = 3.

f(x) = 1/xa = 3k = 3

c₃ =

6.Hard

Find the coefficient c₄ of (x − 2)⁴ in the Taylor series of f(x) = e^2x about a = 2.

f(x) = e^2xa = 2k = 4

c₄ =

Answer key

1. n = 23
2. S₂₂ = 1243
3. L = 1.667
4. S = 1.562
5. c₃ = −0.01235
6. c₄ = 36.4

Full step-by-step solutions: practise this topic on examproblems.com.