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Answer:

1st term: -3

2nd term: 6

3rd term: 21

4th term: 42

Step-by-step explanation:

This problem is unclear if I need to find the first 4 terms or the 4th term. I'm going to assume both possibilities.

To find the value of a term n, you'd just have to plug in that value n into the equation. When finding the first four terms of a sequence, you have to plug in the numbers 1, 2, 3, 4. When you plug in those numbers, you get those said answers.

1st term: 3(1^2)-6=-3

2nd term: 3(2^2)-6=6

3rd term: 3(3^2)-6=21

4th term: 3(4^2)-6=42

When assessing this problem, it is a geometric sequence with a common multiplier.

EXPLANATION:

Given that an = 3n²-6

Put n = 1 then

a1 = 3(1)²-6

⇛a1 = 3(1)-6

⇛a1 = 3-6

⇛a1 = -3

Put n=2 then

a2 = 3(2)²-6

⇛a2 = 3(4)-6

⇛a2 = 12-6

⇛a2 = 6

Put n = 3 then

a3=3(3)²-6

⇛a3 = 3(9)-6

⇛a3 = 27-6

⇛a3 = 21

Put n=4 then

a4 = 3(4)²-6

⇛a4 = 3(16)-6

⇛a4 = 48-6

⇛a4 = 42

Answer: The four terms of the sequence are -3,6,21,42

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