Question

Write an explicit formula for a_na
n
​
, the n^{\text{th}}n
th
term of the sequence 29, 20, 11, ...29,20,11,....

Answer 1

Explicit formula for the sequence 29,20,11....... is $a_n=38-9n$

Given :

term of the sequence 29, 20, 11, ...

We need to find out the formula for the nth term of the given sequence

Lets find out whether the given sequence is arithmetic or geometric

In the given sequence , common difference is 9

$20-29=-9\\11-20=-9$

we can say difference =-9

General explicit formula

$a_n=a_1+(n-1)d$

where a1 is the first term

common difference d=-9

substitute the values

$a_n=a_1+(n-1)d\\a_n=29+(n-1)(-9)\\a_n=29-9n+9\\a_n=38-9n$

Explicit formula for the sequence 29,20,11....... is $a_n=38-9n$

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