Question

a question again #3

Answer 1

\[a _{1},a _{2},a _{3},...\] is a geometric sequence where
\[\sum_{n=1}^{\infty} a _{n} = 4\]
what is the maximum value of \[a _{2}\]

P.S. Hope you can get it within 10 minutes or less, if not give me your medal. lol

Answer 2

maximize \[r(4-4r) = 4r- 4r^2\]

Answer 3

-8r + 4 = 0

r = -4/-8 = 1/2

Answer 4

a = 4 - 2 = 2

ar = 1

Answer 5

Could you explain how you get that result @moneybird?

Answer 6

cool :)

Answer 7

the formula for infinite geometric series is \[\frac{a}{1-r}\]For this case, the sum is 4\[\frac{a}{1-r} = 4 \implies a = 4 - 4r\]\[a_2 = (4-4r) r\]

Answer 8

Ohhh thank you!