Sequence and series (1)
Algebra
Level
pending
The first term of a finite GP of real numbers is positive, and the sum of the series is negative, then a possible number of terms in the series is
25
21
20
23
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1 solution
Let the first term of the G. P. series be ∣ a ∣ and the common ratio be − ∣ r ∣ (since the sum is negative, the common ratio must also be negative). Sum of n terms of the series is − ∣ r ∣ − 1 ∣ a ∣ ( ( − ∣ r ∣ ) n − 1 ) < 0 ⟹ ( − ∣ r ∣ ) n − 1 > 0 . Hence n must be even. Of all the options, only 2 0 is even. So this is the correct option.