SOLUTION: Please help me in solving this arithmetic sequence.: The 21st term of the arithmetic sequence is -48, and the 33rd term is -84. Find the 101st term.

Click here to see ALL problems on Sequences-and-series

Question 568401: Please help me in solving this arithmetic sequence.: The 21st term of the arithmetic sequence is -48, and the 33rd term is -84. Find the 101st term.
Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website!
Please help me in solving this arithmetic sequence.: The 21st term of the arithmetic sequence is -48, and the 33rd term is -84. Find the 101st term.
===============================
The formula for the n-th term of an arithmetic sequence is:
a_n = a_1 + (n-1)d where a_1 = the 1st term, d = the common difference
The information provided gives us two equations in two unknowns:
a_21 = -48 = a_1 + 20d [1]
a_33 = -84 = a_1 + 32d [2]
Subtract [2] from [1]:
36 = -12d
d = -3
Now substitute back into one of the equations above to get a_1:
-48 = a_1 + 20*-3
a_1 = 12
So the formula is a_n = 12 - 3(n-1) = 15 - 3n
Therefore the 101st term is a_101 = 15 - 3*101 = -288