Given a sequence

[Vincen]

Given a sequence: $$a_1,\ a_2,\ .\ .\ .\ ,\ \ a_{14},a_{15}.$$ In the sequence shown, $$a_n=\ a_{n-1}+k,\ where\ 2\le n\le15$$ and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
$$\left(1\right)\ a_1=24.$$ $$\left(2\right)\ a_8=10.$$

The OA is B .

Experts, how can I solve this DS question. I thought option (1) was sufficient.

[Brent@GMATPrepNow]

a1, a2, a3,...a15
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) a1 = 24
(2) a8 = 10

Target question: How many term in the sequence a1, a2, a3,...a15 are greater than 10?

Given: a(n) = a(n-1)+k, where 2 < n < 15
In other words, each term is derived by taking the term before it and adding k
IMPORTANT: Keep in mind that k can be either a positive or negative number. So, the sequence may be increasing (e.g., 5, 7, 9, 11...) or it may be decreasing (e.g., 20, 15, 10, ...)

Statement 1: a1 = 24
The 1st term is 24, but since we don't know the value of k, there's no way to determine the terms in the sequence that are greater than 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a8 = 10
Let's consider the 2 possible cases for k (k is POSITIVE or k is NEGATIVE)

case a: k is POSITIVE
This means that the sequence is INCREASING.
In other words, term1 < term2 < term3, etc.
The 8th term is 10, which means every term after the 8th term must be greater than 10.
So, terms 9, 10, 11, 12, 13, 14 and 15 are greater than 10.
This means that 7 terms in the sequence are greater than 10

case b: k is NEGATIVE.
This means that the sequence is DECREASING.
In other words, term1 > term2 > term3, etc.
The 8th term is 10, which means every term before the 8th term must be greater than 10.
So, terms 1, 2, 3, 4, 5, 6 and 7 are greater than 10.
This means that 7 terms in the sequence are greater than 10

Since BOTH cases yield the SAME answer to the target question, we can be certain that 7 terms in the sequence are greater than 10
Statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent