Question

Write an explicit formula for the sequence 7, 2, -3, -8, -13 then find a14

Answer 1

Answer: We have to find the formula which can fit the explicit sequence, the sequence is as follows:

$\begin{gathered} 7,2,-3,-8,-13 \\ \end{gathered}$

We have to take the 7 as the first term and -13 as the fifth term, we can have the following mathematical formula which can predict the term for any n:

$\begin{gathered} a(n)=7-(n-1)5 \\ \\ \\ a(n)=7-5n+5=12-5n \\ \\ \\ --------------------------- \\ \\ a(n)=-5n+12\Rightarrow(1) \end{gathered}$

Using the formula (1) the 14th term in the sequence is predicted as follows:

$\begin{gathered} a(14)=-5(14)+12=-70+12=-58 \\ \\ \\ a(14)=-58 \end{gathered}$

Therefore the answer is a_14 = -58.