119k views
2 votes
For the following arithmetic sequences find the explicit formula and the value of the indicated term

For the following arithmetic sequences find the explicit formula and the value of-example-1

1 Answer

1 vote
Answer:
\begin{gathered} \text{Explicit formula: a}_n=\text{ -0.2 - 0.4n} \\ a_(15)=\text{ -6.2} \end{gathered}Explanations:

This is an Arithmetic Progression.

The common difference is calculated as follows:


\begin{gathered} d=T_2-T_1 \\ d\text{ = -1.0 - (-0.6)} \\ d\text{ = -1.0+0.6} \\ d\text{ = -0.4} \end{gathered}

The first term, a = -0.6

The explicit formula can be calculated using the formula for the nth term of an Arithmetic Progression.


\begin{gathered} a_n_{}=\text{ a + (n-1)d} \\ a_n=\text{ -0.6 + (n-1)(-0.4)} \\ a_n=-0.6\text{ -0.4n + 0.4} \\ a_n=\text{ -0.6 + 0.4 -0.4n} \\ a_n=\text{ -0.2 -0.4n} \end{gathered}

The explicit formula is therefore:


a_n=\text{ -0.2 - 0.4n}

To get the value of a15, substitute n = 15 into the explicit formula gotten above


\begin{gathered} a_(15)=\text{ -0.2 - 0.4(15)} \\ a_(15)=\text{ -0.2-}6 \\ a_(15)=\text{ }-6.2 \end{gathered}

User Peter Featherstone
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories