Asked by Jeremey
Ѵ7 + Ѵ28 + Ѵ63 + ... +p =300Ѵ7
How many terms are in the sequence?
How many terms are in the sequence?
Answers
Answered by
Reiny
Ѵ7 + Ѵ28 + Ѵ63 + ... +p =300Ѵ7
√7 + 2√7 + 3√7 + .. + p = 300√7
1 + 2 + 3 + .. + p = 300
looks like an arithmetic series with
a = 1, d = 1, n = ? and S<sub>n</sub> = 300
but S<sub>n</sub> = (n/20[2a + (n-1)d]
(n/2)[2 + n-1] = 300
n(1+n) = 600
n^2 + n - 600 = 0
(n+25)(n-24) = 0
n = -25 or n = 24
but n stands for the number of terms, thus has to be positive
So you have 24 terms
√7 + 2√7 + 3√7 + .. + p = 300√7
1 + 2 + 3 + .. + p = 300
looks like an arithmetic series with
a = 1, d = 1, n = ? and S<sub>n</sub> = 300
but S<sub>n</sub> = (n/20[2a + (n-1)d]
(n/2)[2 + n-1] = 300
n(1+n) = 600
n^2 + n - 600 = 0
(n+25)(n-24) = 0
n = -25 or n = 24
but n stands for the number of terms, thus has to be positive
So you have 24 terms
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