Question

Terms of geometric sequence are found by the formula T₁ = arn-1 . if a = 3 and r = 2, find the first 4 terms of the sequence.​

Answer 1

Answer: 3, 6, 12, 24

Step-by-step explanation

The nth term formula for this geometric sequence is
`T_n = 3(2)^(n-1)`

Let's plug in n = 1

`T_n = 3(2)^(n-1)\\\\T_1 = 3(2)^(1-1)\\\\T_1 = 3(2)^(0)\\\\T_1 = 3(1)\\\\T_1 = 3\\\\`

This helps confirm the first term is 3. It also helps confirm we have the correct geometric formula.

Now try n = 2.

`T_n = 3(2)^(n-1)\\\\T_2 = 3(2)^(2-1)\\\\T_2 = 3(2)^(1)\\\\T_2 = 3(2)\\\\T_2 = 6\\\\`

The second term is 6. A shortcut would be to double the previous term (3) to get 6.

If we double the second term, then we get the third term is 6*2 = 12

Notice how:

`T_n = 3(2)^(n-1)\\\\T_3 = 3(2)^(3-1)\\\\T_3 = 3(2)^(2)\\\\T_3 = 3(4)\\\\T_3 = 12\\\\`

Then finally use the formula or the shortcut to determine the 4th term is 24.

In summary, the first four terms are: 3, 6, 12, 24