Describe The Following Sequence. -2 6 -18 54 ....calculator

This guide explains how to analyze and extend the sequence -2, 6, -18, 54... using our calculator and step-by-step explanation.

Identifying the Pattern

The sequence -2, 6, -18, 54... appears to follow a pattern where each term is multiplied by a certain factor to get the next term. Let's examine the relationships between consecutive terms:

From -2 to 6: Multiply by -3 (6 ÷ -2 = -3)
From 6 to -18: Multiply by -3 (-18 ÷ 6 = -3)
From -18 to 54: Multiply by -3 (54 ÷ -18 = -3)

This suggests a geometric sequence where each term is multiplied by -3 to get the next term.

The Formula

The general formula for a geometric sequence is:

aₙ = a₁ × r^(n-1)

Where:

aₙ = nth term
a₁ = first term (-2 in this sequence)
r = common ratio (-3 in this sequence)
n = term number

For our sequence:

aₙ = -2 × (-3)^(n-1)

Extending the Sequence

Using the formula, we can find the next terms in the sequence:

Term (n)	Calculation	Value
1	-2 × (-3)^0	-2
2	-2 × (-3)^1	6
3	-2 × (-3)^2	-18
4	-2 × (-3)^3	54
5	-2 × (-3)^4	-162
6	-2 × (-3)^5	486

The extended sequence is: -2, 6, -18, 54, -162, 486...

Common Mistakes

When analyzing sequences, it's easy to make these common errors:

Assuming an arithmetic pattern when it's geometric
Incorrectly identifying the common ratio
Miscounting the term positions (n)
Forgetting to account for negative signs in calculations

FAQ

Is this sequence arithmetic or geometric?

This is a geometric sequence because each term is multiplied by a constant ratio (-3) to get the next term.

How do I find the 10th term of this sequence?

Use the formula aₙ = -2 × (-3)^(n-1) with n = 10. The 10th term would be -2 × (-3)^9 = -2 × 19683 = -39366.

Can this sequence be extended infinitely?

Yes, the sequence can be extended infinitely by continuing to multiply each term by -3.