The number pattern 1, 5, 11, 19, … is such that the sequence of 'second differences' is a constant.

Determine the 5th number in the pattern.

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Let us consider the series.

`1,5,11,19..........`

We can derive the following relationship among the terms.

`T_2 = 5 = 1+4 = T_1+4`

`T_3 = 11 = 5+6 = T_2+6`

`T_4 = 19 = 11+8 = T_3+8`

According to the pattern;

`T_5 = T_4+10 = 19+10 = 29`

*So the 5th term of the series is 29.*

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