Question

complete the sequence 1,2,10,37,101......

Answer 1

1,2,10,37,101,...
We can write this series as follows:
0³+1=1
1³+1=2
2³+1³+1=10
3³+2³+1³+1=37
4³+3³+2³+1³+1=101
5³+4³+3³+2³+1³+1=226
∴, the next term of the given series is 226. Ans.

Answer 2

Answer:

The next term in the sequence 1, 2, 10, 37, 101...... is 226.

To find:

The next term  of the sequence given.

Solution:

If we observe clearly of the sequence 1, 2, 10, 37, 101......

$\begin{aligned} 1 + 1 ^ { 3 } & = 2 \\\\ 2 + 2 ^ { 3 } & = 10 \\\\ 10 + 3 ^ { 3 } & = 37 \\\\ 37 + 4 ^ { 3 } & = 101 \\\\ 101 + 5 ^ { 3 } & = 226 \\\\ 226 + 6 ^ { 3 } & = 442 \end{aligned}$

And so on  

So, in this series cube of the numbers starting from 1, 2, 3…. are added along with the previously obtained number to get the next term in the series.

Hence, the next term in the sequence 1, 2, 10, 37, 101...... is 226.