Question 993264
Determine the number of terms in an arthmetic 
sequence with t3= -17.5 and t10= -52.5. the 
final term in the sequence is -147.5
<pre>
{{{t[n]}}}{{{""=""}}}{{{t[1]+(n-1)d}}}

Substitute n=3 and t<sub>3</sub>=-17.5

{{{t[3]}}}{{{""=""}}}{{{t[1]+(3-1)d}}}

{{{-17.5}}}{{{""=""}}}{{{t[1]+2d}}}

Substitute n=10 and t<sub>10</sub>=-52.5

{{{t[10]}}}{{{""=""}}}{{{t[1]+(10-1)d}}}

{{{-52.5}}}{{{""=""}}}{{{t[1]+9d}}}

Now we have a system of equations:

{{{system(t[1]+2d-17.5,t[1]+9d=-52.5)}}}

Solve that system and get t<sub>1</sub>=-7.5, d=-5

the final term in the sequence is -147.5

Substitute t<sub>1</sub>=-7.5, d=-5 and t<sub>n</sub>=-52.5
in the same formula

{{{-52.5}}}{{{""=""}}}{{{-7.5+(n-1)(-5)}}}

Solve that and get n = 10

Edwin</pre>