a(1), a(2), a(3), , a(15). In the sequence shown above, a(n)

Question

a(1), a(2), a(3), ……, a(15).

In the sequence shown above, a(n) = a(n-1) + k, where 2 <= n <= 15 and k is a non-zero constant. How many terms in the sequence are greater than 10?

1) a(1) = 24

2) a(8) = 10

abhijit_sen · Answer

k is the most important factor here, so to solve this question we need value of k. So question is how to get k.

Statement 1:
Tells us only 1 value of series, so we will not be able to calculate value of k. As minimum of 2 values are required to calculate k.

Statement 2:
Again Tells us only 1 value of series, so we will not be able to calculate value of k. As minimum of 2 values are required to calculate k.

Statement 1 and 2 together tells us 2 values in series, so we will be able to calculate k. In term we will be able to get all other values in series.

Answer C.

jimmyjamesdonkey · Answer

I thought it was C as well, but this posting says B. Thoughts? https://www.manhattangmat.com/forums/post9641.html#9641

abhijit_sen · Answer

On second thought is quite possible. As a(8) can be expressed as a(1) + some thing + k,
similarly all other terms.

a(1) does not give you a(2), a(3) etc....
But a(8) will give you relative terms so yes now it makes sense, but in haste I ignored it.

FN · Answer

this should be B

here is why

1) says a(1)=24..well first of all series is defined for n>=2...

which means a(2)=a1+K..well for all i know K could be some negative integer..or a positive integer..i just dont know insuff...

2) a(8)=10..which means a(8)=a(7)+K=10

a(7)=10-k
 I know the sequence is till n=15..

i know that A(9)=A(8)+k >10 since K is some non-zero constant..i know that A(n)>K if K were negative to sill be able to give me a 10...sufficient

Brindusa · Answer

It's definetely B.

A is clearly insufficient.
For B we have 2 situations:
1.if K>0 all the numbers from a(9) to a(15) inclusive are >10
2. if K<0 all the numbers from a(1) to a(7) inclusive are >10
So, either way, there are 7 numbers that are greater than 10.

ksh013 · Answer

Pls explain why:

1.if K>0 all the numbers from a(9) to a(15) inclusive are >10
2. if K<0 all the numbers from a(1) to a(7) inclusive are >10

I haven't got

yellowjacket · Answer

ksh013,

We are given a(n) = a(n-1) + k
If k is positive, then the value of a(n) will be greater than a(n-1). Or, the value of each succesive term will be greater than the term that precedes it.

Given a(8) = 10 in B.

For k>0, a(9) > a(8), a(10)>a(9) and so on..

So, for k>0, all the numbers from a(9) to a(15) inclusive are >10.

If k<0, then the value of a(n-1) will be greater than a(n).

Given a(8) = 10 in B.

For k<0, a(7) > a(8), a(6)>a(7) and so on..

So, for k<0, all the numbers from a(1) to a(7) inclusive are >10.

ksh013 · Answer

yellowjacket,

thanks for clear and prompt explanation !

mymba99 · Answer

yupp that was nice explanation.thanks

a(1), a(2), a(3), , a(15). In the sequence shown above, a(n)

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