Answer:
Finding the nth Term of an Arithmetic Sequence
Given an arithmetic sequence with the first term a1 and the common difference d , the nth (or general) term is given by an=a1+(n−1)d .
Example 1:
Find the 27th term of the arithmetic sequence 5,8,11,54,... .
a1=5, d=8−5=3
So,
a27=5+(27−1)(3) =83
Example 2:
Find the 40th term for the arithmetic sequence in which
a8=60 and a12=48 .
Substitute 60 for a8 and 48 for a12 in the formula
an=a1+(n−1)d to obtain a system of linear equations in terms of a1 and d .
a8=a1+(8−1)d→60=a1+7da12=a1+(12−1)d→48=a1+11d
Subtract the second equation from the first equation and solve for d .
12=−4d−3=d
Then 60=a1+7(−3) . Solve for a .
60=a1−2181=a1
Now use the formula to find a40 .
a40=81+39(−3)=81−117=−36 .
See also: sigma notation of a series and nth term of a geometric sequence
Step-by-step explanation:pa brainlist po
