Answer:
We get tₙ: [tex]\mathbf{t_n=an}[/tex]
10th term is [tex]t_{10}=10a[/tex]
Step-by-step explanation:
The given arithmetic sequence is: a,2a,3a
We need to find tₙ and tenth term
Finding tₙ
The formula used is: [tex]t_n=t1+(n-1)d[/tex]
We need to find d, the common difference
a₁ = a
a₂ = 2a
We can find common difference using the formula:
[tex]t_n=t_1+(n-1)d\\Put\:n=2\\t_2=t_1+(2-1)d\\2a=a+d\\d=2a-a\\d=a[/tex]
So, we get common difference d = a
Now, finding tₙ
[tex]t_n=t_1+(n-1)d\\t_n=a+(n-1)a\\t_n=a+an-a\\t_n=an[/tex]
So, we get tₙ: [tex]\mathbf{t_n=an}[/tex]
Now, finding 10th term
By putting n=10 in the equation [tex]t_n=an[/tex]
[tex]t_n=an\\Put\:n=10\\t_{10}=a(10)\\t_{10}=10a[/tex]
So, 10th term is 10a
