Question 1145696
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In the arithmetic sequence (or arithmetic progression) {{{ a[1] }}}, {{{a[2]}}},{{{a[3]}}},... 

each {{{a[j]}}} is related to the previous {{{a[j-1]}}} by a common difference, d.

This means we can write the progression as:

{{{ a[1] }}}, {{{a[1]+d}}}, {{{a[1]+2d }}}, ..., {{{ a[k] = a[1]+(k-1)d }}}, ...

You are given {{{ a[3] }}} = -1  and  {{{ a[7] = -13 }}}

{{{ a[3] = a[1]+2d = -1 }}}
{{{ a[7] = a[1]+6d = -13 }}}

Subtracting the {{{a[3]}}} expression from the {{{a[7]}}} expression:
 {{{ 4d = -12 }}}  --> d = -3

With the common difference, you can easily find {{{a[1] = 5}}} and then write

{{{ a[n] = 5 - 3(n-1) }}}  for n = 1,2,3,...

If you plug in n=22 you will find {{{a[22]}}}


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EDITed to fix the display of the arithmetic progression (commas inside curly braces seem to break things).