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.

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
RELATED QUESTIONS
Find the 21st term of an arithmetic sequence whose first term is 9x and whose common... (answered by mananth)

The 15th and 21st terms of an arithmetic sequence are -67 and -97, respectively. What is... (answered by jamiya,MathTherapy)

please help me solve this challenge question on arithmetic sequences: if the 9th term of... (answered by Maths68)

in an arithmetic sequence, a3=-8 and a17=48 find the 20th term for the... (answered by ewatrrr,rahulsoni001002)

Please help me with this problem: The 15th term of an arithmetic sequence is 74, and the (answered by stanbon)

The seventh term of an arithmetic sequence is 25. Its first, third, and 21st term form... (answered by greenestamps)

Algebra:Arithmetic Sequence "can you plz. help me on this problem what is the... (answered by ewatrrr)

The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th... (answered by ikleyn,Fombitz)

Suppose that the eighth term of an arithmetic sequence is 59, and also suppose that the... (answered by mananth)