A certain series of numbers has 15 terms in total. The first term of the sequence is -4. From the second term, every...

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Tue Sep 01, 2020 9:52 am

E-GMAT

A certain series has 15 terms in total. The first term is -4. From the second term, every even numbered term is 3 more than the previous term, and every odd numbered term is 2 less than the previous term. How many terms are positive in the given series?

A. 7
B. 8
C. 9
D. 10
E. 11

OA B

Solution:

Let a_n be the nth term where n = 1, 2, … 15. So we have:

a_1 = -4
a_2 = -4 + 3 = -1
a_3 = -1 - 2 = -3
a_4 = -3 + 3 = 0
a_5 = 0 - 2 = -2
a_6 = -2 + 3 = 1
and so on.

In other words, the 8 odd-numbered terms are: -4, -3, -2, -1, 0, 1, 2, and 3, and the 7 even- numbered terms are: -1, 0, 1, 2, 3, 4, and 5. We see that there are 3 positive terms among the odd numbered terms and 5 positive terms among the even numbered terms. In total, there are 3 + 5 = 8 positive terms in this sequence.

Answer: B