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
kak​12345678910

The arithmetic sequence 10, 6, 2, −2, … ends with the term −26. How many terms n does it have?

a₁ = 10d = −4aₙ = −26
n =
2.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=2∞ 8·(3/4)ᵏ.

a = 8r = 3/4k₀ = 2
S =
3.Medium
kSn​12345678910S = ?

Find the sum S = Σk=1∞ 1/(k(k + 4)).

ak = 1/(k(k + 4))
S =
4.Medium
AΣ 1/√kk = 1 … ∞BΣ k³/2ᵏk = 1 … ∞CΣ (3/2)ᵏk = 1 … ∞DΣ k!/2ᵏk = 1 … ∞

Exactly one of the four series converges. Click it.

A: Σ 1/√kB: Σ k³/2ᵏC: Σ (3/2)ᵏD: Σ k!/2ᵏ
  1. 1A: Σ 1/√k
  2. 2B: Σ k³/2ᵏ
  3. 3C: Σ (3/2)ᵏ
  4. 4D: Σ k!/2ᵏ
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 4 at x = 0.3. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = sin xn = 4x = 0.3M = 1
|R₄| =
6.Hard

f(x) = cos x is approximated by its Maclaurin polynomial of degree 4 at x = 1. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₄|.

f(x) = cos xn = 4x = 1M = 1
|R₄| =

Answer key

  1. 1. n = 10
  2. 2. S = 18
  3. 3. S = 0.5208
  4. 4. B: Σ k³/2ᵏ
  5. 5. |R₄| = 2.025 × 10⁻⁵
  6. 6. |R₄| = 0.008333

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