TMUA Sequences & Series

Question 1

The first term of an arithmetic sequence is 3 and the common difference is 5. What is the 10th term?

Accepted Answer

48

Answer

The nth term of an arithmetic sequence is a + (n-1)d = 3 + 9×5 = 48.

Question 2

In a geometric sequence, the first term is 2 and the common ratio is 3. What is the 5th term?

Accepted Answer

162

Answer

The nth term of a geometric sequence is ar^(n-1) = 2 × 3^4 = 2 × 81 = 162.

Question 3

What is the sum of the first 20 terms of an arithmetic series with first term 4 and common difference 3?

Accepted Answer

650

Answer

S_n = n/2 × (2a + (n-1)d) = 20/2 × (8 + 57) = 10 × 65 = 650.

Question 4

Which of the following sequences is arithmetic?

Accepted Answer

5, 8, 11, 14, ...

Answer

5, 8, 11, 14 has a constant common difference of 3, making it arithmetic.

Question 5

The nth term of a sequence is given by T_n = 2n² − n + 1. What is the value of T_4?

Accepted Answer

29

Answer

T_4 = 2(4²) − 4 + 1 = 32 − 4 + 1 = 29.

(TMUA) Test of Mathematics for University Admission Practice Test