3.1.1
From the given terms, we can create the following equations:
2𝑥 - 1 = 𝑎
𝑥 + 5 = 𝑎 + 𝑑
4𝑥 - 1 = 𝑎 + 2𝑑
Solving these equations simultaneously, we get:
2𝑥 - 1 = 𝑥 + 5 - 2
2𝑥 - 1 = 𝑥 + 3
𝑥 = 4
Therefore, the value of 𝑥 is 4.
3.1.2
Substitute 𝑥 = 4 back into the equations to find the first three terms:
2(4) - 1 = 7
4 + 5 = 9
4(4) - 1 = 15
Therefore, the first three terms are 7, 9, and 15.
3.1.3
The general rule of the term can be found by observing the common difference between consecutive terms:
9 - 7 = 2
15 - 9 = 6
Therefore, the general rule of the term is 𝑎 + 𝑑𝑛, where 𝑎 = 7 and 𝑑 = 2.
3.1
If2𝑥 − 1,𝑥 + 5and4𝑥 − 1arethefirstthreetermsofalinearsequence, determine the following:
3.1.1
the value of 𝑥.
(2)
3.1.2
the first three terms.
(1)
3.1.3
the general rule of the term.
(1)
1 answer