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# Find the missing number in the series: 40, 54, 82, ?, 180, 250.

Last updated date: 25th Mar 2023
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Hint:  In any series, numbers are not random. They follow a particular order. We need to keenly
observe the given series to find the relation between terms.

Let the missing number be P.
The given series 40, 54, 82, P, 180, 250.
Let’s observe the relation between numbers in the series. The numbers are in increasing order. So
82 < P < 180.
1. Difference between first number and second number is 54 – 40 = 14
2. Difference between second number and third number is 82 – 54 = 28
3. Difference between the third and fourth numbers is P – 82.
4. Difference between fourth and fifth numbers is 180 – P.
5. Difference between the last two numbers of the series is 250 – 180 = 70.
If we observe these differences they are multiples of 14.
The first difference is 14. The second difference is $14 \times 2 = 28$ .
The fifth difference is 14 $\times$5 = 70
$\Rightarrow$ The third difference will be $P - 82 = 14 \times 3$
$\Rightarrow P - 82 = 42$
$\Rightarrow P = 42 + 82$
$$\therefore$$ The missing value is $$P = 124$$.

Note: We can verify the fourth difference (difference between fourth and fifth terms of the series)
with this P value.
$$\Rightarrow 180 - P = 180 - 124 = 56$$
Fourth difference is $$14 \times 4 = 56$$
Hence verified.