Grade 11 · MCR3U · Functions

MCR3U Sequences and Series Practice Test (with Solutions)

On Martian Lab, sequences and series and financial math are one unit, Discrete Functions, because compound interest is a geometric sequence. The free test is 8 multiple-choice questions on recursive, arithmetic and geometric sequences, series, the binomial expansion and simple and compound interest. Write the formula down first, then substitute.

Free Discrete Functions Practice Test

8 questions, exactly as a free account gets them in the first Discrete Functions test on Martian Lab. Try each one on paper first, then open the answer.

The fifth term in the sequence defined by $t_1 = 3$ , $t_n = t_{n-1} - 4$ is
1. -5
2. -9
3. -13
4. -17
Show answer
c) -13
The sum of the first eight terms of the arithmetic series where $a = -6$ and $d = \dfrac{1}{4}$ is
1. -41
2. -36.75
3. -32.25
4. -4.25
Show answer
a) -41
What is the 15th term of the arithmetic sequence that has $t_2 = -8$ and $t_6 =20$ ?
1. -7
2. 83
3. 81
4. -71
Show answer
b) 83
The general term of a geometric sequence with $t_2 = -9$ and $t_5 = \dfrac{64}{3}$ is
1. $t_n = \dfrac{27}{4}\left(-\dfrac{4}{3}\right)^{n-1}$
2. $t_n = \dfrac{9}{2}\left(-\dfrac{4}{3}\right)^{n-1}$
3. $t_n = (-9)^{n-1}$
4. $t_n = \dfrac{3}{2}\left(-\dfrac{4}{3}\right)^{n-1}$
Show answer
a) $t_n = \dfrac{27}{4}\left(-\dfrac{4}{3}\right)^{n-1}$
How many terms are in the sequence 500, 250, 125, $\ldots$ , 0.976 562 5?
1. 9
2. 10
3. 11
4. 12
Show answer
b) 10
Determine which of the following statements is not true.
1. There are 9 terms in the expansion of $(x + a)^8$ .
2. The sum of the exponents in the expansion of $(x + a)^5$ is 6.
3. The coefficients of the terms in the expansion of $(x + a)^{10}$ can be found from the $n = 10^{\text{th}}$ row.
4. The exponent of $y$ in the expansion of $(x + y)^k$ increases by 1 from left to right.
Show answer
b) The sum of the exponents in the expansion of $(x + a)^5$ is 6.
Where is the best place to put your money in order to make the most interest?
1. into an account that pays 5% simple interest
2. into an account that pays 5% interest, compounded semi-annually
3. into an account that pays 5% interest, compounded quarterly
4. under your pillow
Show answer
c) into an account that pays 5% interest, compounded quarterly
The simple interest on $1000 invested for 10 years at 6% interest is
1. $600
2. $1650
3. $1790.85
4. $970.85
Show answer
a) $600

This Unit on Martian Lab

The lessons go from arithmetic, geometric and recursive sequences to arithmetic and geometric series, Pascal's triangle and binomial expansion, then simple and compound interest and annuities.

Arithmetic Sequences
Geometric Sequences
Recursive Seqences
Arithmetic Series
Geometric Series
Pascal's Triangle & Binomial Expansion
Simple & Compound Interest
Annuities

Then 4 full Discrete Functions practice tests to check yourself.

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Discrete Functions FAQ

What is on an MCR3U sequences and series test?+

Arithmetic, geometric and recursive sequences, arithmetic and geometric series, Pascal's triangle and the binomial theorem, and financial math: simple and compound interest and annuities. The free questions on this page touch every topic except geometric series and annuities.

Where is financial math?+

In this unit. Martian Lab teaches simple and compound interest and annuities as the last lessons of Discrete Functions, so there is no separate financial applications unit.

How do you find a term of an arithmetic sequence from two other terms?+

Write tₙ = a + (n - 1)d for both and subtract. With t₂ = -8 and t₆ = 20, 4d = 28, so d = 7 and a = -15. Then t₁₅ = -15 + 14(7) = 83.

How do you find the general term of a geometric sequence?+

Divide the later term by the earlier one to get a power of r. With t₂ = -9 and t₅ = 64/3, r³ = -64/27, so r = -4/3 and a = 27/4, which gives tₙ = (27/4)(-4/3)ⁿ⁻¹.

What is the difference between simple and compound interest?+

Simple interest is paid on the principal only, I = Prt, so $1000 at 6% for 10 years earns $600. Compound interest is also paid on the interest already earned, and the more often it compounds, the more you end up with.

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