Question

write a recursive formula for the given arithmetic sequence, and then find the specified term.a={4,11,18,...}a_1=Answera_n = a_{n-1} + Answera_8 =Answer

Answer 1

Given:-

`n=\left\lbrace4,11,18,...\right\rbrace`

To find the value of:-

`a_1,a_n,a_8`

So a1 is defined as the first term of the given sequence. so we get,

`a_1=4`

So now we write the formula for the nth term of the sequence, the nth term of the sequence is the addition of the last before term and common difference d. so we get,

`a_n=a_(n-1)+d`

Also now we find the value of a8. So we get,

`\begin{gathered} a_n=a_(n-1)+d \\ a_8=a_(8-1)+d \\ a_8=a_7+d_ \end{gathered}`

So now we find the common difference of the given sequence. so we get,

`\begin{gathered} d=11-4 \\ d=7 \end{gathered}`

So we get the sequence,

`4,11,18,25,32,39,46,53`

So now we get,

`a_8=53`