What is the formula for the nth term for the following sequence: 40, 16, 6.4, 2.56, 1.024, 0.4096?
recall that
4^1=4
4^2=16
4^3=64
But, each term is multiplied by 10,1,.1,... = 10^(2-n)
so, Tn = 4^n * 10^(2-n) = 100 (4/10)^n
40 / (2.5 ^ n-1)
Yeah
Shredder is correct .steve is not correct
Ahem.
40/(2.5^n-1)
= 40*2.5/2.5^n
= 100/2.5^n
= 100 / (10/4)^n
= 100 * (4/10)^n
Steve dat nt it . Try this one . .a/2.5^n -1.0 . To check maybe it goes along wit d ques. And is this ogonna
To find the formula for the nth term of a sequence, we need to look for a pattern or rule that relates the terms of the sequence. One common method is to find the common ratio between successive terms. In this case, we can see that each term is obtained by multiplying the previous term by a constant factor of 0.4.
Let's write out the terms of the sequence, starting with the first term (let's call it a₁):
a₁ = 40
a₂ = 16
a₃ = 6.4
a₄ = 2.56
a₅ = 1.024
a₆ = 0.4096
Observing the sequence, we can see that each term is obtained by multiplying the previous term by 0.4:
a₂ = a₁ * 0.4
a₃ = a₂ * 0.4
a₄ = a₃ * 0.4
a₅ = a₄ * 0.4
a₆ = a₅ * 0.4
So, the general formula for the nth term (where n ≥ 1) can be written as:
an = a₁ * 0.4^(n-1)
In this case, the formula would be:
an = 40 * 0.4^(n-1)
So, if you want to find the 10th term of this sequence, you would substitute n = 10 into the formula:
a₁₀ = 40 * 0.4^(10-1)
a₁₀ = 40 * 0.4^9
a₁₀ = 40 * 0.262144
a₁₀ ≈ 10.486