The general expression for given sequence is:
a_n = 7n+5
Step-by-step explanation:
Given sequence is:
12,19,26,33,...
Here
[tex]a_1 = 12\\a_2 = 19\\a_3 = 26[/tex]
It is given that the sequence is an arithmetic sequence, we have to find the common difference first
[tex]d = a_2 - a_1 = 19-12 = 7\\d = a_3 - a_2 = 26 - 19 = 7[/tex]
The explicit formula for arithmetic sequence is:
[tex]a_n = a_1 + (n-1)d[/tex]
Putting the values of d and a1 we get
[tex]a_n = 12 + (n-1)7\\a_n = 12+ 7n - 7\\a_n = 5+7n[/tex]
The general expression for given sequence is:
a_n = 7n+5
Keywords: Arithmetic sequence, common difference
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