In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2).

Question

In a particular sequence,  a_1  = 2,  a_2  = 4, and  a_n = ( a_{n-1} ) + ( a_{n-2} ). For a particular positive integer k, which could be the pair of k and  a_k ?

J_21 · Answer

can anyone explain why answer is not 6,18 here ??

pintukr · Answer

Given,

an = (an - 1) + (an-2)

So,
a1 = 2
a2 = 4
a3 = 4 + 2 = 6
a4 = 6 + 4 = 10
a5 = 10 + 6 = 16
 a6 = 16 + 10 = 26 
a7 = 26 + 16 = 42...and so on .

So, 1st Blank = 6 
  2nd Blank = 26

Bismuth83 · Answer

1. We are given a sequence of positive whole numbers and are asked  what could be a possible   k ,  a_k   pairing .

2. The possible values for  a_k  aren't large, so we can just list a few terms:

(2) (4) (2 + 4) (4 + 2 + 4) (2 + 4 + 4 + 2 + 4) (4 + 2 + 4 + 2 + 4 + 4 + 2 + 4) ....  \rightarrow  2 4 6 10 16 26 ....

3. 6, 10 and 26 pop up as answers. They are  a_3 ,  a_4 , and  a_6 , respectively. The only  k  that works is 6.

4. So, our answer is  k = 6 ,  a_k = 26 .

HarshaBujji · Answer

a1 = 2,
a2 = 4,
a3 = 6,
a4 = 10,
a5 = 16,
a6 = 26.

So (6,26)

seleniumOxide · Answer

This is the long method , is there any shortcut for this problem ?

sg8595 · Answer

It's basically the sum of previous 2 terms. You just need to hit and try for K=5 and 6 and it won't take more than 30 seconds to get to the correct answer.

poojaarora1818 · Answer

Solution:

Given in the question stem:

1.  a_1  = 2

2.  a_2  = 4

3.  a_n = ( a_{n-1} ) + ( a_{n-2} )(By using this formula we can get to the solution)

a_3  = ( a_{n-1} ) + ( a_{n-2} )= 4 + 2 = 6

a_4  = 6+4 = 10

a_5  = 10+6 = 16

a_6  = 16+10= 26

Hence, the only choices that pair with K and  a_k  are 6 and 26.

In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2).

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

k	\(a_k\)
		5
		6
		10
		12
		18
		26

GMAT Two-part Analysis (TPA) Questions

In a particular sequence a1 = 2, a2 = 4, and an = (an - 1) + (an-2).

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards