find the rules and then complete the sequence
1,2,4,3,9,5,16,7,____,____
please show workings
if the second term has been a 1
I would see a nice pattern
the odd-numbered positions are simply the squares of the natural numbers.
i.e. the first, third, fifth, seventh ...terms are 1,4,9,16,..
then even-numbered positions are simply the odd numbers.
i.e. the second, fourth, 6th, 8th,.. terms are (1),3,5,7,...
if the second is indeed a 2 as you typed it, I see no pattern, that fits all the terms.
Once you get past the second term, the pattern I noted still applies.
4a + 12 = 7a - 9
what is a ?
please show workings
To find the rules and complete the sequence, let's analyze the given numbers:
1, 2, 4, 3, 9, 5, 16, 7, ____, ____
Based on the sequence, it appears that the numbers are alternating between two different patterns. Let's break it down into two sub-sequences:
Sub-sequence 1: 1, 4, 9, 16, ____
Sub-sequence 2: 2, 3, 5, 7, ____
Now let's examine each sub-sequence individually to identify the rules:
Sub-sequence 1 (odd terms: 1, 9, ____):
Observing the square of each odd term, we have:
1^2 = 1, 3^2 = 9, 5^2 = 25
So, the pattern for sub-sequence 1 is that each term is the square of consecutive odd numbers. In this case, the next term should be 7^2 = 49.
Sub-sequence 2 (even terms: 2, 5, ____):
Observing the prime numbers in ascending order, we have:
2, 3, 5, 7
So, the pattern for sub-sequence 2 is that each term is a prime number. In this case, the next term should be the next prime number after 7, which is 11.
Now let's combine the two sub-sequences to complete the sequence:
1, 2, 4, 3, 9, 5, 16, 7, 49, 11
So, the missing terms in the sequence are 49 and 11.