Asked by Olabisiy
The sum of infinity and the second term of a geometric progression are 4 and 1 respectively. Find the, 1 common ratio, 2 the first term.
Answers
Answered by
oobleck
S<sub>∞</sub> = a/(1/r) so
a/(1-r) = 4
ar = 1
divide, and you have
r(1-r) = 1/4
r^2 - r + 1/4 = 0
(r - 1/2)^2 = 0
r = 1/2
so a/2 = 1
a = 2
check: 2/(1 - 1/2) = 4
a/(1-r) = 4
ar = 1
divide, and you have
r(1-r) = 1/4
r^2 - r + 1/4 = 0
(r - 1/2)^2 = 0
r = 1/2
so a/2 = 1
a = 2
check: 2/(1 - 1/2) = 4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.