Arithmatic sequence

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Arithmatic sequence

by Anindya Madhudor » Mon Nov 12, 2012 3:36 pm
a(1), a(2),...., a(15)
In the sequence shown, a(n) = a(n-1) + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
1) a(1)=24
2) a(8)=10

Can someone help me solve the above problem. OA is B.

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by GMATGuruNY » Mon Nov 12, 2012 6:10 pm
Anindya Madhudor wrote:a(1), a(2),...., a(15)
In the sequence shown, a(n) = a(n-1) + k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
1) a(1)=24
2) a(8)=10
.
Statement 1 is clearly insufficient.

Statement 2: a₈ = 10.
If k>0, then the sequence is INCREASING: each term in the sequence is GREATER than the preceding term.
In this case, a₉...a�₅ -- a total of 7 terms -- will be greater than 10.
If k<0, then the sequence is DECREASING: each term in the sequence is LESS than the preceding term.
In this case, a�...a₇ -- a total of 7 terms -- will be greater than 10.
In each case, the number of terms greater than 10 = 7.
SUFFICIENT.

The correct answer is B.
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by nisagl750 » Mon Nov 12, 2012 11:17 pm
S1: Insuff, We don't know K is positive or negative

S2: Suff, If a8 is 10, then either a1, a2, ....a7 (7 terms) will be less than 10 if K>0
or a9,a10,.....a15 (7 terms) will be less than 10 if K<0

Its B