Question

How do you write a rule for the nth term of the arithmetic sequence given `a_5=10`, `a_12=24`?

Answer 1

`n^(th)` term `a_n=2n`

Explanation:

In an arithmetic sequence, if `a_1` is the first term and `d` is the difference between a term and its preceding term, than the `n^(th)` term `a_n` is given by `a_n=a_1+(n-1)d`.

Here, we have `a_5=a_1+4d=10` and `a_(12)=a_1+11d=24`. Subtracting former from latter equation, we get

`7d=14` or `d=14/7=2` and `a_1=10-4d=10-4×2=10-8=2`.

Hence, `a_n=a_1+(n-1)d`

= `2+(n-1)×2=2+2n-2=2n`