Sequences
terms from explicit and recursive formulas, monotonicity of sequences, arithmetic and geometric sequences, sums of initial terms
Exercises are drawn at random from a large bank - every click gives a different set.
Narrow the topic
Solved: 0 of 10
The sequence (aₙ) is defined recursively for n ≥ 1. Determine whether it is increasing, decreasing, constant or not monotonic
a₁ = 0, aₙ₊₁ = aₙ − 9
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the indicated term
a₁ = −9, aₙ₊₁ = −aₙ + 4, a₅ = ?
Give the common ratio of the geometric sequence
−9, −3, −1, …
The numbers below are, in this order, three consecutive terms of an arithmetic sequence. Find x
2x − 1, 3x − 7, −x + 7
Is the sequence (aₙ) geometric?
aₙ = 3ⁿ − 5
The sequence (aₙ) is defined recursively for n ≥ 1 and its first terms are given below. Which formula describes this sequence?
5, −6, 16, −28, …
Compute the indicated term of the sequence
aₙ = −6n + 9, a₂ = ?
The sequence (aₙ) is defined recursively for n ≥ 1. Compute the given sum of its first terms
a₁ = 4, aₙ₊₁ = aₙ + n − 1, a₁ + a₂ + a₃ = ?
Give the amount
Tom is saving up for a bike. In the first month he will put aside 40 zł, and in each next month 5 zł more than in the previous one. How many zlotys will he put aside in month 9?
Give the common difference of the arithmetic sequence
a₆ = −40, a₁₀ = −76
This address is one particular set - everyone who opens it gets exactly the same exercises. Copy the link from the address bar and send it to the class. You can generate a new set at the top of the page.
PhiBoard is a free online whiteboard for maths
These exercises are part of it. On the board itself you can plot a function, write a formula in LaTeX, or solve a problem together with a teacher or a friend - live, in the browser. Our app is completely free.