Sash143 wrote:
Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), a_2 = 5, and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A) 4t
B) t^2
C) t^3
D) t^4
E) t^8
Say n = 3 [given n>2]. Hence we must find value of a5
a1 = 3,
a2 = 5,
a3 = 5*3 = 15 = t [an = t given]
a4 = 15*15
a5= 15*15*15*15 = t^4
Hello
pushpitkc, hope you are having an awesome gmat weekend
i have a few questons regarding the above solution, so let me break it down in into following clauses
1.) it says "Say n = 3 [given n>2]. Hence we must find value of a5" my question what does \(n\) mean is it the last term ? based on which rule do we concude " If
n = 3 [given n>2]. Hence we must find value of
\(a_5\) i mean why if n = 3 then we need to find \(a_5\) and not for example \(a_6\) ?
2.) if \(a_3 = a_1*a_2 = 3*5 = 15\), then to find \(a_4\) we need to perform following \(a_1*a_2*a_3 = 3*5*15 = 225\)
and following this logic in order to find \(a_5\)we need to do this \(a_1*a_2*a_3*a_4 = 3*5*15*225 = 3375\)
i cant understand why in the solution above to find \(a_5\) we multiply by the same numbers
\(a_5= 15*15*15*15 = t^4\), to find the next term shoudlnt we mupltiply by all previous terms
3.) Also based on this solution \(a_5= 15*15*15*15 = t^4\) why the correct answer is \(t^4\) because there are FOUR numbers 15
? but there could be infinite NUMBERS of 15
And the last question
is it geometric sequence question ?
many thanks for taking time to explain
enjoy the weekend