# Arithmetic Sequence

• Feb 7th 2006, 05:00 AM
machilove
Arithmetic Sequence
In Arithmetic sequence
a13=4;a21=8;a5=?

What will be the answer?? help
• Feb 7th 2006, 06:16 AM
CaptainBlack
Quote:

Originally Posted by machilove
In Arithmetic sequence
a13=4;a21=8;a5=?

What will be the answer?? help

Lets assume this question is: We have an arithmetic progression $\displaystyle \{a_i,\ i=1,2,..\}$, and $\displaystyle a_{13}=4$ and $\displaystyle a_{21}=8$. What is $\displaystyle a_5\ ?$

Given that $\displaystyle \{a_i,\ i=1,2,..\}$ is an arithmetic progression we know that $\displaystyle a_n=a_1+(n-1)d$, where $\displaystyle a_1$ is the first term, and $\displaystyle d$
is the common difference.

So:

$\displaystyle a_{13}=a_1+12d=4$

and:

$\displaystyle a_{21}=a_1+20d=8$

Subtracting the first of these from the second gives:

$\displaystyle 8d=4$, so $\displaystyle d=1/2$.

Substituting this value for $\displaystyle d$ back into one of the equations gives $\displaystyle a=-2$.

So:

$\displaystyle a_5=-2+4 \times (1/2) =0$

RonL