Question 1054498
Find the value of the following summation:<pre>{{{sum((2n-5),n=15,47)}}}{{{""=""}}}

We write out the first few terms, and the last term:

[2(15)-5] + [2(16)-5)] + [2(17)-5] + [2(18)-5] + ... + [2(47)-5}

[30-5] + [32-5] + [34-5] + [36-5] + ... + [94-5]

25 + 27 + 29 + 31 + ... + 89

We see this is an arithmetic series, with a<sub>1</sub> = 25,
d = 2, and a<sub>n</sub> = 89

We first use the nth term formula to find n:

{{{a[n]}}}{{{""=""}}}{{{a[1]+(n-1)d}}}

{{{89}}}{{{""=""}}}{{{25+(n-1)2}}}

{{{89}}}{{{""=""}}}{{{25+2(n-1)}}}

{{{89}}}{{{""=""}}}{{{25+2n-2}}}

{{{89}}}{{{""=""}}}{{{2n+23}}}

{{{66}}}{{{""=""}}}{{{2n}}}

{{{33}}}{{{""=""}}}{{{n}}}

Then we use the sum formula:

{{{S[n]}}}{{{""=""}}}{{{expr(n/2)(a[1]+a[n])}}}

{{{S[33]}}}{{{""=""}}}{{{expr(33/2)(25+89)}}}

{{{S[33]}}}{{{""=""}}}{{{1881}}}

Answer: 1881

Edwin</pre><b>