7,9,15,57,? find next missing series
Answers
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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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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