Question

How do i write an equation to find thr nth term ouof the sequence 1,3,5,7 then find a24

Answer 1

from 1, to 3, to 5 to 7, notice, is simply adding 2 to get the next term.

1+2 =3, 3+2 =5 and so on.

so the common difference is 2, and the first term is of course 1.

$\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1\\ d=2\\ n=24 \end{cases} \\\\\\ a_{24}=1+(24-1)2\implies a_{24}=1+(23)2\implies a_{24}=1+46\implies a_{24}=47$