Predicting What Comes Next: Sequences and Progressions | Exercise 8.1

Question 4

Which term of the sequence tn=5n−3t_n = 5n - 3 for n≥1n \ge 1 is 607?

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Solution

We will find the position of the term 607 in the given sequence.

Step 1 — Form an equation

Let's say the nn-th term is 607. The formula for the nn-th term is tn=5n−3t_n = 5n - 3. We set the formula equal to 607.

5n−3=6075n - 3 = 607

5n=607+35n = 607 + 3

5n=6105n = 610

n=6105n = \frac{610}{5}

n=122\boxed{n = 122}

Diagram 1

Step 2 — Identify the term

The value of nn is 122. This means 607 is the 122nd term.

Answer

(i) The 122nd term of the sequence is 607.

More questions in Exercise 8.1

Q1

Find the first five terms of the sequence in which the nthn^{\text{th}} term is given by, for n≥1n \ge 1:

(i) tn=3n−4t_n = 3n - 4

(ii) tn=2−5nt_n = 2 - 5n

(iii) tn=n2−2n+3t_n = n^2 - 2n + 3

Q2

Find the 10th10^{\text{th}} and 15th15^{\text{th}} terms of the sequence tn=5n−3t_n = 5n - 3 for n≥1n \ge 1.

Q3

Determine whether 97 and 172 are terms of the sequence tn=5n−3t_n = 5n - 3 for n≥1n \ge 1.

Q4

Which term of the sequence tn=5n−3t_n = 5n - 3 for n≥1n \ge 1 is 607?

Q5

A sequence is given by the recursive rule t1=−5t_1 = -5, tn+1=tn+3t_{n+1} = t_n + 3 for n≥1n \ge 1. Find the first five terms of the sequence. Is 52 a term of this sequence? If so, which term is it?

Q6

Let T1=1T_1 = 1, T2=2T_2 = 2, T3=4T_3 = 4, and Tn=Tn−1+Tn−2+Tn−3T_n = T_{n-1} + T_{n-2} + T_{n-3} for n≥4n \ge 4. Find T4,T5,T6,T7,T_4, T_5, T_6, T_7, and T8T_8.

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