TMUA Sequences & Series 3

Question 1

The nth term of a sequence is T_n = 3n − 2. For what value of n does T_n = 46?

Accepted Answer

16

Answer

Setting 3n − 2 = 46 gives 3n = 48, so n = 16.

Question 2

The sum of the first n terms of a series is S_n = 2n² + 3n. What is the 5th term?

Accepted Answer

21

Answer

T₅ = S₅ − S₄ = (50+15) − (32+12) = 65 − 44 = 21.

Question 3

Three consecutive terms of an arithmetic sequence sum to 30 and their product is 750. What is the middle term?

Accepted Answer

10

Answer

Let the terms be a−d, a, a+d; their sum 3a = 30 gives a = 10, and 10(100−d²) = 750 gives d = ±5, confirming the middle term is 10.

Question 4

The first three terms of a geometric sequence are x+2, 3x, and 5x+4. What is the common ratio?

Accepted Answer

2

Answer

Setting (3x)² = (x+2)(5x+4) gives x = 4, yielding the terms 6, 12, 24 with ratio 2.

Question 5

What is the sum of the first 8 terms of the geometric series 3 + 6 + 12 + ...?

Accepted Answer

765

Answer

S₈ = 3(2⁸ − 1)/(2 − 1) = 3 × 255 = 765.

(TMUA) Test of Mathematics for University Admission Practice Test