Question

the first 3 terms of the arithmetic sequence are given. find an expression t_ n in the terms of n and write the tenth term of each sequence​

Answer 1

We get tₙ:
`\mathbf{t_n=an}`

10th term is
`t_(10)=10a`

Explanation:

The given arithmetic sequence is: a,2a,3a

We need to find tₙ and tenth term

Finding tₙ

The formula used is:
`t_n=t1+(n-1)d`

We need to find d, the common difference

a₁ = a

a₂ = 2a

We can find common difference using the formula:

`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`

So, we get common difference d = a

Now, finding tₙ

`t_n=t_1+(n-1)d\\t_n=a+(n-1)a\\t_n=a+an-a\\t_n=an`

So, we get tₙ:
`\mathbf{t_n=an}`

Now, finding 10th term

By putting n=10 in the equation
`t_n=an`

`t_n=an\\Put\:n=10\\t_(10)=a(10)\\t_(10)=10a`

So, 10th term is 10a