SOLUTION: 1.) Find the indicated term using the given information: a20=45, a10=25, a1=? 2.) Find the sum of the infinite geometric series: -10,-5,-5/2?

Algebra ->  Sequences-and-series -> SOLUTION: 1.) Find the indicated term using the given information: a20=45, a10=25, a1=? 2.) Find the sum of the infinite geometric series: -10,-5,-5/2?      Log On


   

Question 969332: 1.) Find the indicated term using the given information: a20=45, a10=25, a1=?
2.) Find the sum of the infinite geometric series: -10,-5,-5/2?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B20%5D=a%5B1%5D%2B20d=45
a%5B10%5D=a%5B1%5D%2B10d=25
Subtract the second equation from the first,
a%5B1%5D%2B20d-a%5B1%5D-10d=45-25
10d=20
d=2
Then,
a%5B1%5D%2B10%282%29=25
a%5B1%5D%2B20=25
a%5B1%5D=25-20
a%5B1%5D=5
.
.
.
Look at the ratio of successive terms,
-5%2F-10=1%2F2
-5%2F2%2F-5=1%2F2
So each subsequent term is the previous term divided by 2.
-10%2F2=-5
-5%2F2
-5%2F4
-5%2F8
-5%2F16
.
.
.