Next term in SeQuEnCe

Logic Level 2

$\large 4, 15, 40,85 , \_\_$

Find the next term in the sequence above.

2 solutions

. .
Apr 30, 2021

$4 = 1 ^ { 3 } + 1 ^ { 2 } + 1 + 1$

$15 = 2 ^ { 3 } + 2 ^ { 2 } + 2 + 1$

$40 = 3 ^ { 3 } + 3 ^ { 2 } + 3 + 1$

$85 = 4 ^ { 3 } + 4 ^ { 2 } + 4 + 1$

$a = 5 ^ { 3 } + 5 ^ { 2 } + 5 + 1 = 125 + 25 + 5 + 1 = 156$

Louis Ullman
Apr 22, 2018

$4=(2+0)\cdot (2)\\ 15=(2+1)\cdot (2+3)\\ 40=(2+2)\cdot (2+3+5)\\ 85=(2+3)\cdot (2+3+5+7)\\ \boxed { 156 } =(2+4)\cdot (2+3+5+7+9)$

Can the next term be (2+4)(2+3+5+7+11)=168,because 2,3,5,7,11 are primes?

X X - 3 years, 1 month ago

This can also be represented as n^3+n^2+n+1.

Siva Budaraju - 3 years, 1 month ago