Question

Find the value of the 14th term in the arithmetic sequence.-2,1,4,7,10,...(14th term)

Answer 1

Given the sequence;

`-2,1,4,7,10,...`

The nth term of an arithmetic sequence is;

`\begin{gathered} a_n=a_1+(n-1)d \\ \\ Where\text{ }a_1=first\text{ }term,d=common\text{ }difference \end{gathered}`

The common difference, d, is the difference between the consecutive terms of an arithmetic sequence.

`\begin{gathered} d=a_2-a_1 \\ \\ Where\text{ }a_2=second\text{ }term \end{gathered}`

Given;

`\begin{gathered} a_2=1,a_1=-2 \\ \\ d=1-(-2) \\ \\ d=3 \end{gathered}`

Thus, the 14th term is;

`\begin{gathered} n=14,d=3,a_1=-2 \\ \\ a_(14)=-2+(14-1)(3) \\ \\ a_(14)=-2+(13)(3) \\ \\ a_(14)=-2+39 \\ \\ a_(14)=37 \end{gathered}`

ANSWER: 37