Q21. - Algebra 1

Question

Find the next three terms in each sequence.

$5,5,6,8,11,15,\mathrm{....}$

Step-by-Step Solution

Answer

The next three terms are 20, 26 and 33.

Step 1. Find the common difference of the corresponding terms.

Calculate the common difference between the corresponding terms to find the pattern of the sequence.

$\begin{array}{c}{a}_2-a_1=5-5=0\\ a_3-a_2=6-5=1\\ a_4-a_3=8-6=2\\ a_5-a_4=11-8=3\\ a_6-a_5=15-11=4\end{array}$

Step 2. Find the trend of the given sequence.

Notice that the difference between each corresponding terms are $0,1,2,3\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}4$.

 

Thus the difference is increasing by 1 in each next terms.

 

Step 3. Find the next three terms.

Following the pattern the next three terms are calculated as follows.

$$\begin{gathered} a_7-a_6=5 \\ a_7=a_6+5 \\ =15+5 \\ a_7=20 \\ {a}_8-a_7=6 \\ a_8=a_7+6 \\ =20+6 \\ a_8=26 \\ {a}_9-a_8=7 \\ a_9=a_8+7 \\ =26+7 \\ a_9=33 \end{gathered}$$

Therefore, the next three terms of the given sequence are 20, 26 and 33.