How do you find the sum of the arithmetic sequence $5+11+17+...+95$ ?

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Answer 1 · 2017-01-05T14:14:59

$:." The Reqd. Sum ="800$ .

We know that the sum $S_n$ of first $n$ terms of an Arithmetic

Sequence is given by,

$S_n=n/2(a+l)$ , where, $a and l$ are the first term and the last

(i.e., $n^(th)" term "T_n$ ) of the Seq.

So, let $l=T_n=95$

We know that, $T_n=a+(n-1)d$ .

In our Problem,

$a=5, l=95, and, d=11-5=17-11=...=6$ .

$:. T_n=75 rArr 5+6(n-1)=95 rArr n=16$

Therefore, $S_n=S_16=16/2(5+95)$ .

$:." The Reqd. Sum ="800$ .

How do you find the sum of the arithmetic sequence 5+11+17+...+955+11+17+...+95?