SOLUTION: The first three terms of an arithmetic series are 60, 4p and 2p – 6 respectively. Show that p = 9 Find the value of the 20th term of this series. Prove that the sum of the

Algebra ->  Sequences-and-series -> SOLUTION: The first three terms of an arithmetic series are 60, 4p and 2p – 6 respectively. Show that p = 9 Find the value of the 20th term of this series. Prove that the sum of the      Log On


   

Question 940801: The first three terms of an arithmetic series are 60, 4p and 2p – 6 respectively.
Show that p = 9
Find the value of the 20th term of this series.
Prove that the sum of the first n terms of this series is given by the expression
12n (6 – n)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Difference between successive terms is a constant.
4p-60=2p-6-4p
6p-60=-6
p-10=-1
highlight%28p=9%29

The three terms are: 60, 36, 12
Common difference is -24.

General term, highlight%2860-%28n-1%2924%29.
n is the index for the term.


The general term is usually stated as A%5B1%5D%2B%28n-1%29d, but you know from your specific example that d=-24, so subtraction is shown for the general term of your example. You would evaluate 60-%2819%29%2824%29.