Question 46737
You can find the value of the nth term in an arithmetic sequence using the formula {{{u[n]=a+(n-1)d}}}
Where {{{u[n]}}} is the nth term,
a = the value of the first term,
d = the difference between two consecutive terms.
Let's look at the 7th term:
{{{u[7]=a+6d=16}}}.............1
Mow the 61st term:
{{{u[61]=a+60d=232}}}...........2
Solve equations (1) and (2) to find a and d.
Multiply equation (1) by 10:
{{{10a+60d=160}}}.............3
subtract (2) from (3):
{{{9a=160-232=-72}}}
{{{a=-72/9}}}
{{{a=-8}}}................4
Now plug a=-8 into equation 1:
{{{-8+60d=160}}}
{{{60d=168}}}
{{{d=2.8}}}
Now we know a and d, we can use the formaula to find the 100th term.
{{{u[100]=-8+99(2.8)=269.2}}}
I hope this helps,
Adam
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