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Sagot :
There are 6 terms in the sequence greater than 1.
What is a geometric series ?
A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
To know more about Geometric Series
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