Question 909056
How many terms of the arithmetic sequence
 -3,2,7,...
must be added together the sum of the series to be 116?
What is the equation for this arithmetic sequence?
Explain your process.


 arithmetic sequence has a {{{common}}} {{{difference}}} {{{d}}}

the recursive formula for an arithmetic sequence is written in the form {{{a[n]=a[n-1]+d}}}

Rather than write a recursive formula, we can write an explicit formula. The explicit formula is also sometimes called the closed form. To write the explicit or closed form of an arithmetic sequence, we use 

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

in this case {{{-3}}},{{{2}}},{{{7}}},.... {{{d=5}}}

check:
{{{-3+5=2}}}
{{{2+5=7}}}

so, next one is {{{7+5=12}}}

{{{-3}}} ,{{{2}}}, {{{7}}} ,{{{12}}},{{{17}}},{{{22}}},{{{27}}},{{{32}}},{{{37}}},{{{42}}}.... 

How many terms must be added together the sum of the series to be {{{116}}}, we can find out by adding

{{{  -3+2+7+12+17+22+27+32=116}}}

so, the answer is: we need first {{{8}}} terms