What is the difference between the sixth and the fifth terms

Question

What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17

Bunuel · Accepted Answer

Given that  a_n=n+2^{n-1} , thus:

a_6=6+2^{6-1}=38 ;
 a_5=5+2^{5-1}=21 ;

The difference is 38-21=17.

Answer: E.

sasyaharry · Answer

Notice that 2 raised to any positive number will aways be even.

Hence the sixth term will be even+even = even 
The fifth term will be odd+even = odd

The only two answers that are odd are B and E. I would say that looking at the sequence we can say that the gap is expanding, hence answer is  E

Bigred2008 · Answer

Just one question, why do they mention 2, 4, 7. Is that to throw a test-taker off?

Bunuel · Answer

2, 4, and 7, are the first, second and the third terms of the sequence whose nth term is n + 2^(n - 1). For n = 1, n + 2^(n - 1) = 1 + 2^0 = 2, for n = 2, n + 2^(n - 1) = 2 + 2^1 = 4, and for n = 3, n + 2^(n - 1) = 3 + 2^2 = 7. So, those numbers are given simply as an example.

ScottTargetTestPrep · Answer

For the sixth term, we need to substitute 6 for n, and for the fifth term, we need to substitute 5 for n. Then we'll find the difference between the two terms.

Let’s first plug 6 in for n.

6 + 2^(6-1)

6 + 2^5

6 + 32 = 38

Next let’s plug 5 in for n.

5 + 2^(5-1)

5 + 2^4

5 + 16 = 21

Thus, the difference between the 6th and 5th term of the sequence is 38 – 21 = 17.

Answer is E.

gjonrexha · Answer

Plug in 6 and 5 for the sixth and fifth sequence respectively.....

Sixth sequence = 6 + 2^(6-1) = 38

Fifth sequence = 5 + 2^(5-1) = 21

38-21
=
17

hiranmay · Answer

What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2^(n - 1)?

(A) 2
(B) 3
(C) 6
(D) 16
(E) 17-->  correct

Analysis: t6-t5 = 6 + 2^5 - 5 -2^4=1+2^4=17

mathislife · Answer

n6 = 6+2^5
n5 = 5+2^4

n6-n5= 6+2^5-(5+2^4)
=1+2^5-2^4
=1+2^4(2-1)
=1+16(1)
=17

MHIKER · Answer

AS,  a_n=n+2^{n-1}

∴ a_6=6+2^{6-1}=38 ;
 ∴ a_5=5+2^{5-1}=21 ;

The difference  =38-21=17

The answer is  E

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=CjSSXIA2l8E

ArnauG · Answer

To find the difference between the sixth and fifth terms of the given sequence, we need to calculate these terms using the provided formula.

The formula for the nth term of the sequence is given as n + 2^(n - 1).

Let's calculate the fifth term:
n = 5
5 + 2^(5 - 1) = 5 + 2^4 = 5 + 16 = 21

Now, let's calculate the sixth term:
n = 6
6 + 2^(6 - 1) = 6 + 2^5 = 6 + 32 = 38

The difference between the sixth and fifth terms is:
38 - 21 = 17

Therefore, the difference between the sixth and fifth terms of the sequence is 17.

The correct answer is (E) 17.

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What is the difference between the sixth and the fifth terms

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What is the difference between the sixth and the fifth terms

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