Find the missing number of the series: 3, 9, 41, 113, __?__, 577
Answers
-3, 9, 41, 113, __265__, 577.
265 is the missing number of the series.
The first term should be -3 intead of 3.
- The sequence followed is that first we note down the difference between the second and first term.
- Next we check the difference between the third and second term.
- We will observe that the difference between the second and first differences increases by a factor of 2.
First term = -3
Second term = 9
Their difference (D₁) = First term - Second term = 9 - (-3) = 9 + 3 = 12
Second term = 9
Third term = 41
Their difference (D₂) = Third term - Second term = 41 - 9 = 32
Difference of the 2 differences = D' = D₂ - D₁ = 32 - 12 =20.
Third term = 41
Fourth term = 113
Their difference (D₃) = 113 - 41 = 72
Difference of the 2 differences = D'' = D₃ - D₂ = 72 - 32 = 40, Which is twice as D'. This is how the sequence goes.
Fourth term = 113
Fifth term = x
Their difference (D₄) = x - 113
Difference of the 2 differences = D''' = D₄ - D₃ = (x-113) - 72 = x - 185.
This difference, D''' should be twice as D'' ( which is 40) as the sequence says.
So, x - 185 = 2(40)
⇒ x = 185 + 80 = 265
Thus, the missing no. is 265 (Fifth term) and D''' = x - 185 = 265 - 185 = 80 (twice of D'')
and D₄ = x - 113 = 265 - 113 = 152
Fifth term = 265
Sixth term = 577
Their difference (D₅) = 577 - 265 = 312
Difference of the 2 differences = D'''' = D₅ - D₄ = 312 - 152 = 160, which is twice as that of the previous difference D''' which was 80.
Therefore, the sequences are satisfied and the missing number is 265.