Question

For each exercise, write the equation you think should come next. Check your prediction with a calculator.

$\begin{array}{l}9\times 9+7=88\\ 98\times 9+6=888\\ 987\times 9+5=8888\end{array}$

Short answer

The next equation must be $9876\times 9+4=88888$.

Step-by-step solution

Step 1. Define deductive and inductive reasoning.

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequence

$\begin{array}{l}9\times 9+7=88\\ 98\times 9+6=888\\ 987\times 9+5=8888\end{array}$

reason inductively that is., we can conclude based on past observations

As,

$\begin{array}{r}9\to 98\to 987\\ 7\stackrel{-1}{\to }6\stackrel{-1}{\to }5\\ 88\to 888\to 8888\end{array}$

And 9 is fixed.

Step 3. Predict the next equation.

So, as per the pattern of the sequence, next terms in the equation will be:

$\begin{array}{r}9\to 98\to 987\to \underset{¯}{9876}\\ 7\stackrel{-1}{\to }6\stackrel{-1}{\to }5\stackrel{-1}{\to }\underset{¯}{4}\\ 88\to 888\to 8888\to \underset{¯}{88888}\end{array}$

Therefore, the next equation must be $9876\times 9+4=88888$.