a_15 = 90
a_n = 6n
Step-by-step explanation:
Given sequence is:
6, 12, 18, 24,...
First of all we have to find the common difference. The common difference is the difference between consecutive terms of an arithmetic sequence.
Here,
[tex]d=a_2-a_1 = 12-6 = 6\\d=a_3-a_2= 18-12 = 6[/tex]
The general form for arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]
Putting the values for a_1 and d
[tex]a_n=6+(n-1)(6)\\a_n=6+6n-6\\a_n=6n[/tex]
a) Find a15
[tex]a_{15} = 6(15)\\=90[/tex]
b) Write an equation for the nth term.
The equation is: a_n=6n
Keywords: Arithmetic sequence, Common Difference
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