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.

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1.Easy

The arithmetic sequence −8, −11, −14, −17, … ends with the term −86. How many terms n does it have?

a₁ = −8d = −3aₙ = −86

n =

2.Easy

The arithmetic sequence 20, 18, 16, 14, … ends with the term −14. How many terms n does it have?

a₁ = 20d = −2aₙ = −14

n =

3.Medium

Find the sum S = Σ_k=1^∞ 6/(k(k + 3)).

a_k = 6/(k(k + 3))

S =

4.Medium

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

a_k = 1/(k(k + 1))

S =

5.Hard

Recognise the series and find its sum: S = Σ_k=0^∞ (−1)ᵏ·2^2k+1/(2k + 1)!.

a_k = (−1)ᵏ·2^2k+1/(2k + 1)!

S =

6.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 5 at x = 0.8. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₅|.

f(x) = sin xn = 5x = 0.8M = 1

|R₅| =

Answer key

1. n = 27
2. n = 18
3. S = 3.667
4. S = 1
5. S = 0.9093
6. |R₅| = 0.0003641

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