Question 211762This question is from textbook COLLEGE ALGEBRA
: Pls help
1/125, 1/25, 1/5.....to 7term
• Write the next 3 terms,
• Find the indicated tn,
• Find the indicated Sn.
This question is from textbook COLLEGE ALGEBRA
Found 2 solutions by stanbon, RAY100:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1/125, 1/25, 1/5.....to 7term
• Write the next 3 terms,
Multiply by 5 to get 1,5,25
----------------------------------
• Find the indicated tn,
t(n) = 5^(n-4)
----------------------------------
• Find the indicated Sn.
S(n)= [5^(n+1)-1]/(5-1)
The n was not specified so the sum is not determined.
==========================================================
Cheers,
Stan H.
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website! 1/125,1/25,1/5,......
.
appears to be a geometric series, with a multiple of (1/ 1/5) or 5
.
The basic form is ,,,a(n) = a(1)r^(n-1),,with a(1) = 1/125, and r=5
.
check,,,1st term,,,a(1) = 1/125 * 5^(1-1) = 1/125,,,,ok
,,,,,,,,2 nd term,,a(2) = 1/125 * 5^(2-1) = 1/25,,,,ok
,,,,,,,,3 rd term,,a(3) = 1/125 *5^(3-1) = 1/5,,,,,ok
.
,,,,,,,,4 th term ,,a(4) = 1/125 *5^(4-1)= 1
,,,,,,,,5 th term,,,a(5) = 1/125 *5^(5-1) = 5
,,,,,,,,6 th term ,,a(6) = 1/125 *5^(6-1) = 25
.
,,,,,,,,7 th term ,,a(7) = 1/125 * 5^(7-1) = 125,,,,,t(n)
.
The sum of a geometric series is, S=a(1) [ (1-r^n) /(1-r) ]
.
In this case S(7) = (1/125) [ ( 1-5^7) / (1-5) ]
.
S(7) = (1/125) [ (-78124) / (-4)]
.
S(7) = (1/125) [ 19531]
.
s(7) = 156.248
.
.
check,,,adding the individual terms above = 156.248,,,,ok
|
|
|
