What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

Question

Aicharya · Accepted Answer

The pattern is $n^3 + n^2 + n$: $1^3+1^2+1 = 3$, $2^3+2^2+2 = 14$, $3^3+3^2+3 = 39$, $4^3+4^2+4 = 84$, $5^3+5^2+5 = 155$, $6^3+6^2+6 = 258$. Hence the missing term is 155.

What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

Solution