The terms of the sequence {An}, where n is a positive intege

Question

The terms of the sequence {A n }, where n is a positive integer, satisfy A 1 =81, A 2 =82, A 3 =83, and A n+3 =A n +4. Which of the following cannot be a value of A n ?
 
A. 801 
B. 802 
C. 803 
D. 804 
E. 805

Leo8 · Accepted Answer

Sequence = 81,82,83, 85,86,87, 89,90,91, 93,94,95, 97,98,99, 101,102,102,..

Every 4th number is missing :After every 3 numbers, the number jumpy by 2 :

so we don't have 84,92,96,100,..... : This is in AP with an increment of 4.

So we know numbers divisible by 4 cannot be there in the given series

Test the numbers :

1. 801 - This is not divisible by 4
2. 802 - This is not divisible by 4
3. 803 - This is not divisible by 4
 4. 804 - This is divisible by 4 
5. 805 - This is not divisible by 4

MathRevolution · Answer

=>

The terms of the sequence can be divided into three groups: 
A 1  = 81, A 4  = 85, A 7  = 89, … : These have a remainder of 1 when they are divided by 4.
A 2  = 82, A 5  = 86, A 8  = 90, … : These have a remainder of 2 when they are divided by 4.
A 3  = 83, A 6  = 87, A 9  = 91, … : These have a remainder of 3 when they are divided by 4.
No term of the sequence is a multiple of 4.

Since 804 is a multiple of 4, it cannot be a term of the sequence.

Therefore, the answer is D.

Answer: D

testcracker · Answer

hi

very new to sequence

can you please tell me how you have arrived at the sequential order (81,82,83, 84,85,86, 89,90,91, 93,94,95, 97,98,99, 101,102,102..) ?

thanks in advance

Leo8 · Answer

Hi - Sorry there is a correction in the my post - we will not have term 84 in the series

The terms of the sequence {An}, where n is a positive integer, satisfy A1=81, A2=82, A3=83, and An+3=An+4. Which of the following cannot be a value of An?

A1 = 81, A2 = 82, A3 = 83

to derive A4 - we will use the formula given : A(1+3) = A1 + 4 : 
so A4 = 81 + 4 = 85, 
likewise A5 = A2 + 4 = 82 + 4 = 86
A6 = A3 + 4 = 83 + 4 = 87

as you can see there is a jump of 2 unit after every 3rd number..

hence the sequence is : 81, 82, 83, 85, 86, 87, 89, 90, 91,

testcracker · Answer

hi
thank you, + 1

please let me first understand what the formula given "An+3 = An + 4" really means ?

how can "An + 4" and "An + 3" be the same number, and how did you get A (1 + 3) = An + 4

thanks

Leo8 · Answer

gmatcracker2018

The formula is given in the question as a representation of nth number

by A(1 + 3) - I meant A(n +3)th term can be expressed in terms of Anth term + 4 or

every (n + 3)th term is addition of nth term and the number 4

testcracker · Answer

thanks a lot, again +1

please know that I am very new to sequence problem, so please guide through my explanation

we are given
A1 =81, A2 = 82 and A3 = 83

and also there is formula, "An+3 = An + 4" to find A4 or any subsequent number in the sequence

now since we are to find out A4, we can let n = 1

thus A( 1 + 3 ) = A1 + 4

A4 = 81 + 4 = 85

and when to find A5 we can set n to equal to 2

A( 2 + 3 ) = A2 + 4

=) a5 = 82 + 4 = 86

In the same way, to find A6, we have to let, n = 3

A (3 + 3) = A3 + 4

=) a6 = 83 + 4 + 87

and a7 = A (4 + 3) = a4 + 4

=) 85 + 4 = 89

so we have

a4 = 85
a5 = 86
a6 = 87
a7 = 89

and so on ...

thus it is evident that multiples of 4 are missing
so, the number, 804 cannot be a value of An

I think this is what you wanted to mean ?
is that okay?

thanks in advance, man

bumpbot · Answer

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The terms of the sequence {An}, where n is a positive intege

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