Question

Given the nth term for each arithmetic sequence, how to find the indicated term here? (1) `a_n=6n+1; a_12` (2) `a_n=3n-5; a_20`

Answer 1

1) 73
2) 55

Explanation:

1) `a_(color(red)(n)) =6color(red)(n)+1`

For `a_12` where ever there is an `color(red)(n)` write 12 giving:

`a_12=6(12)+1 color(white)("d") ->color(white)("d")a_12=[6xx12]+1=73`

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2) `a_color(red)(n)=3color(red)(n)-5`

For `a_color(red)(20)`where ever there is an `color(red)(n)` write 20 giving:

`a_color(red)(20)=3(color(red)(20))-5color(white)("d")->color(white)("d")a_20=[3xx20]-5=55`