Question 1103995
<pre><b>
{{{a[n]}}}{{{""=""}}}{{{a[1]+(n-1)d}}}

Substitute n = 13, d = 7

{{{a[13]}}}{{{""=""}}}{{{a[1]+(13-1)(7)}}}

{{{a[13]}}}{{{""=""}}}{{{a[1]+(12)(7)}}}

{{{a[13]}}}{{{""=""}}}{{{a[1]+84}}}

Substitute a<sub>13</sub> = 241

{{{241}}}{{{""=""}}}{{{a[1]+84}}}

Subtract 84 from both sides

{{{157}}}{{{""=""}}}{{{a[1]}}}

Back to

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

Substitute a<sub>1</sub> = 157, d = 7

{{{a[n]}}}{{{""=""}}}{{{157+(n-1)(7)}}}

{{{a[n]}}}{{{""=""}}}{{{157+7(n-1)}}}

{{{a[n]}}}{{{""=""}}}{{{157+7n-7}}}

{{{a[n]}}}{{{""=""}}}{{{7n+150}}} <--explicit formula

To find first five terms, write first term 157, and
add 7 successively to it and each preceding term to get the
next term:

157, 164, 171, 178, 185  <--first five terms

Edwin</pre>