Question

What is the missing number in the series 41, 42, 45, 43, 54, 51, 79, 78, __, 142?​

Answer 1

Missing number (?) = 128

Step-by-step explanation:

The given series are:

41, 42, 45, 43, 54, 51, 79, 78, ____, 142

To find, the missing number (?) in the given series = ?

The given series have two sequences.

First sequence (odd places):

41, 45, 54, 79, ____

The pattern follow:

Previous number + $2^2$, Previous number + $3^2$, Previous number + $5^2$, ......

Where, 2, 3, 5,7 are consecutive prime numbers

45 = 41 + $2^2$ = 41 + 4 = 45

54 = 45 + $3^2$ = 45 + 9 = 54

79 = 54 + $5^2$ = 54 + 25 = 79

? = 79 + $7^2$ = 79 + 49 = 128

Second sequence (even places):

42, 43, 51, 78, 142

The pattern follow:

Previous number + $1^3$, Previous number + $2^3$, Previous number + $3^3$, Previous number + $4^3$, ............

43 = 42 +  $1^3$ = 42 + 1 = 43

51 = 43 +  $2^3$ = 43 + 8 = 51

78 = 51 + $3^3$ = 51 + 27 = 78

142 = 78 +  $4^3$ = 78 + 64 = 142

∴ Missing number (?) = 128