Question

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

Answer 1

Step-by-step 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

Answer 2

Answer:

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

Step-by-step explanation: