Infinite sequence

by **Capthan** Tue Jul 22, 2008 8:28 am

The infinite sequence a1, a2,...,an is defined such that an = (n+2) / n for all n ≥ 1. What is the product of the first 10 terms of the sequence?

(A) 45
(B) 66
(C) 90
(D) 121
(E) 132

by **Amit** Tue Jul 22, 2008 2:29 pm

132 i guess

by **Capthan** Wed Jul 23, 2008 5:43 am

The answer is B

by **rfernandez** Sat Jul 26, 2008 5:22 am

Capthan, what is the source of this question? Is it from one of the Math Strategy Guides? It does not ring a bell.

If you do not post the source, we will need to delete the question from the forum. If it is not from one of the Math Strategy Guides, it should not be posted on this forum. And if it's from one of the banned sources identified in the sticky, then it should not be posted anywhere on our forums. Thanks.

by **Capthan** Sun Jul 27, 2008 6:28 am

Rey
This one too a question from MGMAT 250 extremely challenging quantitative problems. please help me on this one.
Thnanks

by **Guest** Tue Jul 29, 2008 2:28 am

Sequence is
(n+2)/n

It is equal to 1+2/n

Putting numbers in we get

a1 = 1 + 2/1 = 1 + 2 = 3
a2 = 1 + 2/2 = 1 + 1 = 2
a3 = 1 + 2/3 = 5/3
a4 = 1 + 2/4 = 6/4

etc

Lining them all up and multiplying

3 * 2 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12
- - - - - - - -
3 4 5 6 7 8 9 10

Denominators cancel the numerators

5,6,7,8,9,10 in denominators cancel themselves in the numerators, and 3 and 4 in the denominator take out the 12

and you get

3 * 2 * 11

= 66

by **rfernandez** Fri Aug 08, 2008 4:50 am

Nice solution, guest.