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#.