Question 275375
what is the sum of the integers between 20 and 480 that are multiples of 11? 
please use the equation needed, thank you:)
<pre><font size = 4 color = "indigo"><b>
The first term is 22 and we can find the last term by dividing

{{{480}}} by {{{11}}}, getting {{{43&7/11}}} So {{{43*11}}} or {{{473}}} is the
last term.

The multiples of {{{11}}} are {{{11}}} apart, so we have an arithmetic
sequence for which the common difference, {{{d}}} is {{{11}}}.

The formula for the sum which we need is this:

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

where {{{a[1]=22}}} is the first term and {{{a[n]=473}}} is the last
term.

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

But we need {{{n}}}, so we first need the formula for the nth term:

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

{{{473=22+(n-1)*11}}}

{{{473=22+11(n-1)}}}

{{{473=22+11n-11}}}

{{{473=11+11n}}}

{{{462=11n}}}

{{{42=n}}}

No we can substitute 

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

where {{{n=42}}}, {{{a[1]=22}}} and {{{a[n]=a[22]=473}}} 

{{{S[42]=(42/2)(22+473)}}}

{{{S[42]=(21)(495)}}}

{{{S[42]=10395}}}

Edwin</pre>