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12,14,18,26,42 what are the next 2 numberso in the sequence

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Logic: (Each sequence adds up to double)

12,14,18,26,42....

12, (12+2),14 (14+4) , 18 (18+8), 26 (26+16), 42 (42+32), 74 (74+64), 138

Answer:

the next 2 numbers are 74 and 138
User Millebii
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Power is the result of multiplying two numbers together. The next two terms of the sequence are 74 and 138.

What is power?

Power is the result of multiplying two numbers together. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.

The given sequence of number if observed then every next number of the series can be written as the sum of the pervious term and the power of 2. Therefore, we can write it as,

a₁ = 12

a₂ = a₁ + 2¹ = 12 + 2 = 14

a₃ = a₂ + 2² = 14 + 4 = 18

a₄ = a₃ + 2³ = 18 + 8 = 26

a₅ =a₄ + 2⁴ = 26 + 16 = 42

Thus, Generalizing the terms, we can express any term of the series as,

aₙ = a₍ₙ₋₁₎ + 2⁽ⁿ⁻¹⁾

Further, 5 terms are already given, therefore, the sixth and the seventh term of the sequence are,

a₆ = a₍₆₋₁₎ + 2⁽⁶⁻¹⁾

= a₅ + 2⁵

= 42 + 32

= 74

a₇ = a₍₇₋₁₎ + 2⁽⁷⁻¹⁾

= a₆ + 2⁶

= 74 + 64

= 138

Hence, the next two terms of the sequence are 74 and 138.

User Amr Alaa
by
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