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Algebra Level 3

Find the next number that will continue the given series: 2, 12, 36, 80, ?

Note : assume each term follows a 3rd degree polynomial with integer coefficients.


The answer is 150.

Rohit Gupta by rohit gupta , 27, India

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1 solution

Method 1.
1 3 + 1 = 2 1^3+1=2
2 3 + 4 = 12 2^3+4=12
3 3 + 9 = 36 3^3+9=36
4 3 + 16 = 80 4^3+16=80
5 3 + 25 = 150 5^3+25=\boxed{150}


Method 2.
1 3 + 1 2 = 2 1^3+1^2=2
2 3 + 2 2 = 12 2^3+2^2=12
3 3 + 3 2 = 36 3^3+3^2=36
4 3 + 4 2 = 80 4^3+4^2=80
5 3 + 5 2 = 150 5^3+5^2=\boxed{150}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I think both are same method.

rohit gupta - 5 years, 6 months ago

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Yes,both are same but in 1st method odd no. are added. And in second meathod cubes and squares are added.

A Former Brilliant Member - 5 years, 6 months ago

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