Question

12,36,80,150,252,? find the next number in series​

Answer 1

Ans. Series is 2, 12, 36, 80, 150, ?

Step -I Difference b/w steps of given series -

10, 24, 44, 70, X (let diff b/w 150 & ? is X)

Step -II Difference b/w series of steps I-

14, 20, 26, Y (let diff b/w 70 & X is Y)

Step III Difference b/w series of Step II-

6, 6, 6 ( Here 6 is common diff b/w all steps)

now,

Step II will be - 14, 20, 26, 32 ( Because Y = 26+6)

Step I will be- 10, 24, 44, 70, 102 ( Because X = 70+32)

therefore given series will be-

2, 12, 36, 80, 150, 252 ( Because ? = 150+102)

So answer is 252.

Answer 2

Answer:

Next number is 252. 

nth term is n³ + n²

Step-by-step explanation:

or another method  2 = 1. 2 

12 = 2 . 6 = 4 .3 

36 = 3. 12 = 9 .4 

80 = 5 . 4^2 = 16 .5 

150 = = 25 .6 

A(n) = = n^2 .(n + 1) 

next 

A(6) = 6^2 .7 =36 .7 = 252