Question

what number will replace the ?
7,9,15,57,?​

Answer 1

Given :- what number will replace the ?

• 7,9,15,57, ?

Solution :-

since numbers are in increasing order , checking multiple first,

→ 7 * 1 + 2 = 7 + 2 = 9

→ 9 * 2 - 3 = 18 - 3 = 15

→ 15 * 4 - 3 = 60 - 3 = 57

we can conclude that, multiply pattern is in GP ( 1, 2, 4 then next will be 8) and addition and subtraction is in order of (+2, -3, -3, +2) .

then, next term will be,

→ 57 * 8 + 2 = 456 + 2 = 458 (Ans.)

checking difference between terms now,

7 9 15 57 ?

2 6 42

as we can see that difference pattern is :-

→ 2 = 1 * 2

next,

→ 6 = 2 * 3 .

and,

→ 42 = 6 * 7

then, next difference will be,

→ 48 = 7 * 8 .

therefore,

→ Next term in the series = 57 + 48 = 105 (Ans.)

Hence, Both 105 and 458 can replace the " ? " .

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Answer 2

Given :  7,9,15,57,?

To find :  next missing series​

Solution:

7, 9, 15, 57, ?

7  + (1 !)²  + 1 !  = 7  +  1 + 1  = 9

9  + (2 !)²  + 2 !  = 9  +  4 + 2  = 15

15  + (3 !)²  + 3 !  =15  +  36 + 6  =  57

57 +   (4 !)²  + 4 !  =57  +  576 + 24  =  657

Hence next number is 657

Tₙ₊₁ = Tₙ + (n!)² + (n!)      or Tₙ₊₁ = Tₙ +  (n!)(n! + 1)  

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