Question

Find the next term of the given series: $17,27,37,56,66,...$.

Answer 1

Calculate the next term of the given series

Given series: $17,27,37,56,66,...$.

Observe the sum of the digits of the numbers of the series.

$$\begin{gathered} 1+7=8 \\ 2+7=9 \\ 3+7=10 \\ 5+6=11 \\ 6+6=12 \end{gathered}$$

Thus, the sum of the digits of the next term will be $13$.

All possible terms whose sum of the digits is $13$ are shown below.

$$\begin{gathered} 4+9=13 \\ 5+8=13 \\ 6+7=13 \\ 7+6=13 \\ 8+5=13 \\ 9+4=13 \end{gathered}$$

So, the possible next term of the series is $49,58,67,76,85,94$.

Now let us consider the difference between two consecutive terms of the given series.

$$\begin{gathered} \left(27-17\right)=10 \\ \left(37-27\right)=10 \\ \left(56-37\right)=19 \\ \left(66-56\right)=10 \end{gathered}$$

Thus the difference between first two consecutive terms of the series is $10$

Then the difference between next two consecutive term is $19$

Then again the difference between next two consecutive term is $10$

So the difference in the next term will be $10$

Therefore, the next term can be $76$, as $\left(76-66\right)=10$

Therefore, the next term of the given series is $76$.