Answer :
Answer:
- a) Arithmetic,
- b) t(n) = 16 - 3n.
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We observe that the sequence is decreasing with common difference of - 3.
- 16, 13, 10, 7, 4, 1
Therefore, this is an AP, with the first term of t(1) = 13 and common difference of d = -3.
Use the nth term formula for AP:
- t(n) = t(1) + (n - 1)d
- t(n) = 13 + (n - 1)(- 3) = 13 - 3n + 3 = 16 - 3n
Answer:
a) Arithmetic sequence
b) t(n) = 16 - 3n
Step-by-step explanation:
An Arithmetic Sequence has a constant difference between each consecutive term.
A Geometric Sequence has a constant ratio (multiplier) between each consecutive term.
Part (a)
From inspection of the given table, t(n) decreases by 3 each time n increases by 1. Therefore, the sequence is arithmetic with a common difference of -3.
Part (b)
[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
- a = 13
- d = -3
- aₙ = t(n)
Substitute the initial value (when n = 1) and the common difference into the formula to create an equation for the nth term:
[tex]\implies t(n)=13+(n-1)(-3)[/tex]
[tex]\implies t(n)=13-3n+3[/tex]
[tex]\implies t(n)=16-3n[/tex]