<PRE><B>Question 755524</B>
Q:
sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is
its fifteenth term and common difference.
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A:
In arithmetic sequence, the sum of the first n terms is equal to
{{{S[n]}}} = {{{(n/2)(a[1] + a[n])}}}
The sixth term is {{{a[6]}}} = 27, if the common difference is d then the first term is {{{a[1]}}} = 27 - 5d and the 20th term is {{{a[20]}}} = 27 + 14d.
{{{S[20]}}} = {{{(20/2)(a[1] + a[20])}}}
900 = {{{(20/2)((27 - 5d) + (27 + 14d))}}}
900 = {{{10(9d + 54)}}}
9d + 54 = 90
d = 4
{{{a[1]}}} = 27 - 5(4) = 7
The nth term is {{{a[n]}}} = 7 + 4(n - 1) = 4n + 3
The 15th term is {{{a[15]}}} = 4(15) + 3 = 63
Here are the answers: 
15th term: {{{highlight(63)}}} and common difference, d = {{{highlight(4)}}}</PRE>