Question

If a_1 =2 and a_n = 3a_n-1 - 2 then find the value of a_5.

Answer 1

and

We need to find common difference, in order for us to do that, Let try to find a2.

Remebr a1=2

so a2=

so a2=4.

This means the common difference is 2 because a1 is 2 and a2 is 4.

Now, we use arithmetic formula to find a5

Where a is the inital term, a1

D is common difference and n is the term we trying to find

So we get

So

a_5=10

Explanation:

Answer 2

Explanation:

We know that

`a _(1) = 2`

and

`a _(n) = 3a _(n - 1) - 2`

We need to find common difference, in order for us to do that, Let try to find a2.

`a _(2) = 3a _(2 - 1) - 2`

`a _(2) = 3 a_(1) - 2`

Remebr a1=2

`a _2{} = 3(2) - 2`

so a2=

`6 - 2 = 4`

so a2=4.

This means the common difference is 2 because a1 is 2 and a2 is 4.

Now, we use arithmetic formula to find a5

`a + d(n - 1)`

Where a is the inital term, a1

D is common difference and n is the term we trying to find

So we get

`2 + 2(5 - 1) = 2 + 2(4) = 10`

So

a_5=10