3, 14, 39, 84, ?

M4maths Previous Puzzles

16 May 2011 what will be next

3, 14, 39, 84, ?

OPtion

1) 98
2) 125
3) 150
4) 155
5) 190
6) 175
7) 200
8) 110
9) 115
10) 92

Solution

1^3+1^2+1, 2^3+2^2+2, 3^3+3^2+3, 4^3+4^2+4, 5^3+5^2+5 = 155

Correct Option: 4 Best Solution (14)

~Sandeep~   13 years AGO

The series is based on following formula:
n[(n+1)^2 - n^2
For n=5 i.e. 5th term:
5(5+1)^2 -5^2 = 5*36 -25 = 155 (Option 4)

Like? Yes (6) | No (4)  

Sahil   13 years AGO

5^1+5^2+5^3=5+25+125 =155

Like? Yes (2) | No (1)  

Shiv   13 years AGO

every term is obtained by putting x=1,2,3,4,5
in
x+x^2+x^3
3=1+1+1
..
..
when x=5
5+25+125=155

Like? Yes (3) | No (2)  

Sulekha   13 years AGO

3=1+1^2+1^3
14=2+2^2+2^3
similarly for 39 and 84.

5^3+5^2+5=155

Like? Yes (2) | No (1)  

Khanna   13 years AGO

nth term =Tn== n(n^2 + n + 1)

so 5th term = 5*(5^2+5+1)=5(25+5+1) =5*31=155

Like? Yes (4) | No (4)  

YadeeshKumar   13 years AGO

3 = 1 * 3
14 = 2 * 7
39 = 3 * 13
84 = 4 * 21
155 = 5 * 31

Like? Yes (2) | No (2)  

Meena   13 years AGO

3=1+1^2+1^3
14=2+2^2+2^3
39=3+3^2+3^3
84=4+4^2+4^3
similarly
5+5^2+5^3=5+25+125=155

Like? Yes (2) | No (2)  

MP    13 years AGO

nth term is given by n+n^2+n^3

so here 3=1+1+1
14=2+4+8
39=3+9+27
84=4+16+64

hemce next term will be

5+25+125=155... option 4

Like? Yes (2) | No (2)  

Balakumaran N.A   13 years AGO

T(n) = n[(n+1)^2 - n]
= n(n^2 + 2n + 1 - n)
= n(n^2 + n + 1)
= n^3 + n^2 + n

T(5) = 5(25 + 5 + 1)
= 5 * 31
= 155

Like? Yes (2) | No (2)  

HARMEET KAUR   13 years AGO

we get each term of series by putting value of n as 1,2,3,4,5,6,.....
in
n*[(n+1)^2-n)
as 3= 1*(4-1)
14=2(9-2)
39=3*(16-3)
84=4*(25-4)
hence next term will be 5*(36-5)=5*31=155

Like? Yes (2) | No (2)  

Bawa   13 years AGO

n th term == n(n^2 + n + 1)
3=1*(1+1+1)
14=2*(4+2+1)
..
..
155=5*(25+5+1) =5*31=155

Like? Yes (2) | No (2)  

A.P.Singh   13 years AGO

3, 14, 39, 84, ?
here
Tn = n^3 + n^2 + n
as n=1, Tn =1+1+1=3
T2=8+4+2=14
T3=27+9+3=39
T4..
T5=125+25+5=155

Like? Yes (3) | No (3)  

dharmaveer   13 years AGO

T(n) = n[(n+1)^2 - n]

3 = 1 * 3
14 = 2 * 7
39 = 3 * 13
84 = 4 * 21

and

T(5) = 5(25 + 5 + 1)
= 5 * 31
= 155


option 4.

Like? Yes (2) | No (2)  

Karthik Pandiyan   13 years AGO

Formula : n^3 + n^2 + n
n=1 >> 1+1+1 =3
n=2 >> 8+4+2 =14
n=3 >> 27+9+3 =39
n=4 >> 64+16+4 =84
n=5 >> 125+25+5=155

Like? Yes (1) | No (2)