Question

What is the 19th term
The firsts 3 are 1,-2,4
This is a geometric sequence

Answer 1

262,144

Explanation:

The first three terms of the sequence are 1, -2, and 4. To determine the type of sequence, we can calculate the common ratio, which is the ratio between consecutive terms.

The common ratio between the first two terms is -2/1 = -2. The common ratio between the second and third terms is 4/-2 = -2.

This means that the sequence is a geometric sequence.

The formula for the nth term of a geometric sequence is:

`\boxed{\boxed{\sf a_n = a_1 \cdot r^((n-1))}}`

Where:

• 
  `\sf a_n` is the nth term
• 
  `\sf a_1` is the first term
• r is the common ratio
• n is the term number

In this case,
`\sf a_1= 1`, r = -2, and n = 19.

Substituting these values into the formula, we get:

`\sf a_(19) = 1 \cdot (-2)^((19 - 1))`

`\sf a_(19) = 1 \cdot (-2)^(18)`

`\sf a_(19) = 1 \cdot 262,144`

`\sf a_(19) = 262,144`

Therefore, the 19th term of the geometric sequence is 262,144.

Answer 2

262144

Explanation:

Progression: 1, -2, 4,...

• For it to be arithmetic, there must be a common difference.

• For it to be geometric, there must be a common ratio.

There is no common difference as -2 -1 ≠ 4 -(-2)

-3 ≠ 6

There is a common ratio as 2nd term/1st term = 3rd term/2nd term

-2/1 = 4/-2

-2 = -2 --- -2 is the common ratio

• So it is a geometric progression, formula: ar^{n-1}

Here first term (a) is 1, Common ratio (r) is -2 and nth term is 19.

• So substituting: 1(-2)^{19-1) = 1(-2)^{18} = 262144