# Question

A number sequence is shown below

3,7,3,7,4,3,7,3,7,4,3,7,3,7,4………

What is the sum of the first 126 numbers?

• Look at the number pattern below
 Column A Column B Column C Column D 1 2 3 7 6 5 4 8 9 10 11 15 14 13 12 16 17 18 19 … … … …

In which column will the number ‘909’ appear?

Can anyone help with this problem?

0 Replies 1 Like

First question,
One set has five numbers = 3,7,3,7,4
The sum of one set = 24

Number of sets for  first 126 numbers = 126/5 = 25 remainder 1

The sum of 25 sets = 25 X 24 = 600

The remainder 1 will include 3. which is another 3
Therefore total sum = 600 +3 = 603 ###

2nd question

 A) Remainder 0 or 7 B) Remainder 1 or 6 C) Remainder 2 or 5 D) Remainder 3 or 4 1 2 3 7 6 5 4 8 9 10 11 15 14 13 12 16 17 18 19 23 22 21 20 24 25 26 27

They repeat their rows in cycle of 8. SO just divide by 8, get the remainder and matched the above table to get the column.

909 / 8 = 904 remainder 5.  So it is in column C

0 Replies 3 Likes

When the numbers are divided by 8

 Column A Column B Column C Column D Remainder 0 Remainder 1 Remainder 2 Remainder 3 Remainder 7 Remainder 6 Remainder 5 Remainder 4 Remainder 0 Remainder 1 Remainder 2 Remainder 3 Remainder 7 Remainder 6 Remainder 5 Remainder 4 Remainder 0 Remainder 1 Remainder 2 Remainder 3

909 divided by 8 has a remainder of 5

Therefore, Column C

0 Replies 3 Likes

Q1: 3,7,3,7,4 is 1 set of 5 numbers (sum is 24), then repeated each set.

There are 25 sets (125/5) in 125 numbers (total sum of 25 sets = 24×25=600).

Last number (new set) is 3. Total sum is 600+3=603#

Q2: Assuming there is “0” in column A, in front of “1” in column B.

There is a snake pattern starting from 0 and ending with 7. (1 set of 8 numbers)

There are 909-0+1=910 numbers including “0”.

910 divided by 8 = 113.75, so 113 complete sets.

113 x 8 = 904 numbers in 1st 113 sets (these 904 numbers are 0, 1, 2, … 903)

Remaining numbers are

904             905             906             907

XX             XX             909             908

909 appears in column C#

0 Replies 2 Likes