What is the 20th term of the sequence that begins -2,4,-8,16.....?
a = -2
r = -2
so,
T20 = -2*(-2)^19
To determine the 20th term of the sequence, we need to identify the pattern.
Looking at the sequence -2, 4, -8, 16..., we see that each term is obtained by multiplying the previous term by -2.
To find the 20th term, we start with the first term, -2, and repeatedly multiply by -2:
Term 1: -2
Term 2: -2 * (-2) = 4
Term 3: 4 * (-2) = -8
Term 4: -8 * (-2) = 16
We continue this pattern, multiplying the previous term by -2, until we reach the 20th term.
Term 5: 16 * (-2) = -32
Term 6: -32 * (-2) = 64
...
By continuing this pattern, we eventually find the 20th term.
Term 20: 16 * (-2)^(20-1) = 16 * (-2)^19
Therefore, the 20th term of the sequence is 16 * (-2)^19.
To find the 20th term of the sequence -2, 4, -8, 16..., we can start by analyzing the pattern in the sequence.
From the given terms, we can see that each term is obtained by multiplying the previous term by -2. So, we can write the recursive formula for the sequence as:
a₁ = -2
aᵢ = -2 * aᵢ₋₁, for i > 1
To find the 20th term, we can use this recursive formula and find each term one by one until we reach the 20th term.
Alternatively, we can also use the formula for the nth term of a geometric sequence, given by:
aₙ = a₁ * r^(n-1)
Where a₁ is the first term, r is the common ratio, and n is the desired term number.
In this sequence, the first term (a₁) is -2 and the common ratio (r) is -2. Now, we can substitute these values into the formula:
a₂₀ = -2 * (-2)^(20-1)
= -2 * (-2)^19
= -2 * 2^19
= -2 * 524288
= -1048576
Therefore, the 20th term of the sequence is -1048576.