Interleaved series always come up in the IPAT and are one of the easiest to recognize and solve. Let us try to explain this series type with an example.

1, 2, 5, 3, 9, 4, ?

If we split this series into two series –

1, 5, 9 (consists of the 1^{st} 3^{rd} and 5^{th} numbers – all odd numbered terms)

2, 3, 4 (consists of the 2^{nd} 4^{th} and 6^{th} numbers –all even numbered terms)

We see a simple difference based pattern in both series. The first series has a constant difference of 4 while the second series has a constant difference of 1. The next number in the parent series (which is the 7^{th} term- an odd number) is the next number in the 1^{st} sub series (1,5,9) and hence is equal to 9 + 4 = 13.

**The rule of 1,2,3**

The rule of 1,2,3 gives us a simple to use framework to crack these kind of series questions. The rule goes as follows – form subseries in the given series by first leaving 1 term in between, then 2 terms in between and then 3 terms in between to see which interleaved difference gives a legitimate difference series.

For example, the series above had a subseries gap of 1 term. Here is an example of 2 term subseries

1, 7, 11, 2, 9, 14, 3, 11, 17

Breaking the series into subseries based on 2 term difference

1, 2, 3 (1st, 4th, 7th terms : simple difference series with constant difference of 1)

7, 9, 11 (2nd, 5th, 8th terms : simple difference series with constant difference of 2)

11, 14, 17 (3rd, 6th and 9th terms: simple difference series with constant difference of 3)

Now let’s practice with some IPAT like questions

Q) 7, 6, 14, 12, 21, 18, ?

Solution

7, 14, 21, ? (This is 7×1, 7×2, 7×3)

6, 12, 18 (This is 6×1, 6×2, 6×3)

It is seen that terms in each subseries are multiple of the first number in the subseries. Hence the solution is 7×4 = 28

Q) 2, 3, 4, 4, 9, 16, 16, 81, ?

Solution

2, 4, 16

3, 9, 81

4, 16, ?

We observe the next term in each subseries in the square of the previous term in the same subseries.

Hence the solution is 16×16 = 256

Q) 1, 2, 3, 4, 1.1, 3, 6, 4, 1.21, 4.5, 12, 4, 1.331, ?

Solution

1, 1.1, 1.21, 1.331 ( each next term is formed by multiplying previous term by 1.1)

2, 3, 4.5, ? (each next term is formed by multiplying previous term by 1.5)

3, 6, 12 (each next term is formed by multiplying previous term by 2)

4, 4, 4 (each next term is formed by multiplying previous term by 1)

Consequently, the next term in the series is 4.5×1.5 = 6.75

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