Answer:
The required formula is:
[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]
Step-by-step explanation:
The total number of squares of the the first term = 4
The total number of squares of the the second term = 7
The total number of squares of the the third term = 10
so,
[tex]a_1=4[/tex]
[tex]a_2=7[/tex]
[tex]a_3=10[/tex]
Finding the common difference d
[tex]d=a_3-a_2=10-7=3[/tex]
[tex]d=a_2-a_1=7-4=3[/tex]
As the common difference 'd' is same, it means the sequence is in arithmetic.
So
If the initial term of an arithmetic progression is [tex]{\displaystyle a_{1}}[/tex] and the common difference of successive members is d, then the nth term of the sequence [tex](a_n)[/tex] is given by:
[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]
Therefore, the required formula is:
[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]
