Evaluate variable expressions for arithmetic sequences
key notes:
1. Understanding Arithmetic Sequences
- An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference (d).
- The general form of an arithmetic sequence can be expressed as: an=a1+(n−1)⋅d
where:
- an = the nth term of the sequence
- a1 = the first term of the sequence
- n = the term number
- d = common difference
Learn with an example
🔔 Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
-7n + 3
____ ,____ ,____
To find the 1st term, plug in n = 1.
-7n + 3 = -7(1) + 3 = -7 + 3 = -4
To find the 2nd term, plug in n = 2.
-7n + 3 = -7(2) + 3 = -14 + 3 = -11
To find the 3rd term, plug-in n = 3.
-7n + 3 = -7(3) + 3 = -21 + 3 = -18
The first three terms of the sequence are -4, -11, -18.
🔔 Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
10n + 6
____,____ ,____ ,____
To find the 1st term, plug in n = 1.
10n + 6 = 10(1) + 6 = 10 + 6 = 16
To find the 2nd term, plug in n = 2.
10n + 6 = 10(2) + 6 = 20 + 6 = 26
To find the 3rd term, plug-in n = 3.
10n + 6 = 10(3) + 6 = 30 + 6 = 36
To find the 4th term, plug-in n = 4.
10n + 6 = 10(4) + 6 = 40 + 6 = 46
The first four terms of the sequence are 16, 26, 36, 46.
🔔 Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.
6n + 3
____,____ ,____ ,____ ,____
To find the 1st term, plug in n = 1.
6n + 3 = 6(1) + 3 = 6 + 3 = 9
To find the 2nd term, plug in n = 2.
6n + 3 = 6(2) + 3 = 12 + 3 = 15
To find the 3rd term, plug-in n = 3.
6n + 3 = 6(3) + 3 = 18 + 3 = 21
To find the 4th term, plug-in n = 4.
6n + 3 = 6(4) + 3 = 24 + 3 = 27
To find the 5th term, plug-in n = 5.
6n + 3 = 6(5) + 3 = 30 + 3 = 33
The first five terms of the sequence are 9, 15, 21, 27, 33.
let’s practice!🖊️
