Question

Number 11Find the nth term of each sequence then find a24

Answer 1

`\begin{gathered} a_n=1+(n-1)\cdot2 \\ a_(24)=47 \end{gathered}`

11) Let's firstly examine the sequence:

`\begin{gathered} 1,3,5,7 \\ a_1=1 \\ d=2 \end{gathered}`

Note that the first term is 1, and this sequence goes increasing by 2 units so the common difference is d=2

2) So we can write an Explicit formula for that Arithmetic Sequence, and then find the 24th term:

`\begin{gathered} a_n=a_1+(n-1)d \\ a_(24)=1+(24-1)2 \\ a_(24)=1+23\cdot2 \\ a_(24)=1+46 \\ a_(24)=47 \end{gathered}`

Note that we multiplied the difference by (n-1), in this case, n=24

3) Hence, the 24th term is 47 and the equation is an=1+(n-1)2