Arithmetic Sequence

**machilove** · February 7th 2006, 05:00 AM

In Arithmetic sequence
a13=4;a21=8;a5=?

What will be the answer?? help

**CaptainBlack** · February 7th 2006, 06:16 AM

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 $\{a_i,\ i=1,2,..\}$ , and $a_{13}=4$ and $a_{21}=8$ . What is $a_5\ ?$

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

So:

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

and:

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

Subtracting the first of these from the second gives:

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

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

So:

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

RonL

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