Inspect 5

Inspect the sequence and complete the following statement:

seq: 1, 4, 9, 16, 25, 36, 49

The first two numbers differ by a.
The second and third numbers differ by b.
The third and fourth numbers differ by c.
The difference between any two successive numbers always seems to be more than the preceding difference.
Use inductive reasoning to predict the missing number in the sequence.

Result

a =  3
b =  5
c =  7
d=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a_1=1 \\ {a}_2=4 \\ {a}_3=9 \\ {a}_4=16 \\ {a}_5=25 \\ {a}_6=36 \\ {a}_7=49 \\ {a}_n=n^2 \\ a=a_2-a_1=4-1=3 \end{gathered}$$

$b=a_3-a_2=9-4=5$

$c=a_4-a_3=16-9=7$

$d=1$

Try another example