Question 1022547
.
The sum of the first and last terms of a linear sequence is 42. If the sum of all the terms is 420 and the second term is 4, find {{{highlight(what)}}}.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`


<pre>
Use this formula for the sum of arithmetic progression:

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

(see the lesson <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A> in this site).

Then you get 

{{{420}}} = {{{(42*n)/2}}}  --->   n = 20.

Next, from the condition you have these two equations

{{{a[1]}}} + {{{a[20]}}} = 42,
{{{a[2]}}} = {{{4}}},

or

{{{a[1]}}} + {{{a[1]+19*d}}} = {{{42}}},
{{{a[1]+d}}} = {{{4}}},

or

{{{2a[1]}}} + {{{19d}}} = {{{42}}},
{{{a[1]+d}}} = {{{4}}}.

The solution of this system is {{{a[1]}}} = 2, d = 2.

Get it by any method.

========================================

Do not use the term "a linear sequence".


Use the commonly accepted term "arithmetic progression".
</pre>