Question

What is the next number in sequence 2, 14, 20, 100, 104, ?

Answer 1

Answer:

I think that the answer is 110

Answer 2

• The next number in given sequence will be either 312 or 304 .

To Find :- The next number in sequence 2, 14, 20, 100, 104, ?

Solution (1) :-

Logic :-

• First number × 7 = Second number
• Third number × 5 = Fourth number
• Fifth number × 3 = Sixth number
• We have to multiply each pair by odd numbers in decreasing order .

checking we get,

First number × 7 = Second number

→ 2 × 7 = 14

Third number × 5 = Fourth number

→ 20 × 5 = 100

Fifth number × 3 = Sixth number

→ 104 × 3 = 312 (Ans.)

Solution (2) :-

Logic :-

• given series :- 2, 14, 20, 100, 104
• a(1) = 2
• a(2) = 14
• From third term :- a(n) = {11 - 2 × (n - 2)} × a(n - 2) + (n - 2) + add 1 when n = odd.
• a(3) = (11 - 2 × 1) × a(1) + 1 + 1
• a(4) = (11 - 2 × 2) × a(2) + 2
• a(5) = (11 - 2 × 3) × a(3) + 3 + 1
• a(6) = (11 - 2 × 4) × a(4) + 4

Explanation :-

→ a(1) = 2

→ a(2) = 14

→ a(3) = (11 - 2 × 1) × a(1) + 1 + 1 = (11 - 2) × 2 + 1 + 1 = 9 × 2 + 2 = 20

→ a(4) = (11 - 2 × 2) × a(2) + 2 = (11 - 4) × 14 + 2 = 7 × 14 + 2 = 98 + 2 = 100

→ a(5) = (11 - 2 × 3) × a(3) + 3 + 1 = (11 - 6) × 20 + 3 + 1 = 5 × 20 + 4 = 100 + 4 = 104

then, next number will be,

→ a(6) = (11 - 2 × 4) × a(4) + 4 = (11 - 8) × 100 + 4 = 3 × 100 + 4 = 300 + 4 = 304 (Ans.)

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