10th term of the 4,-6,9 geometric progresion and sulotion
r = -3/2
T10 = 4 * (-3/2)^9
Well, let's calculate the 10th term of the geometric progression with the first term 4 and the common ratio -6/4 (which simplifies to -3/2).
To find the 10th term, we can use the formula for the nth term of a geometric progression:
aₙ = a₁ * r^(n-1)
Where:
aₙ = nth term
a₁ = first term
r = common ratio
n = term number
Plugging in the values:
a₁ = 4
r = -3/2
n = 10
a₁ * r^(n-1)
= 4 * (-3/2)^(10-1)
= 4 * (-3/2)^9
= 4 * (-19683/512)
= -78732/512
≈ -153.75
So, the 10th term of the geometric progression is approximately -153.75.
As for the "sulotion," well, that seems to be a typo. But hey, I'll give you a solution: If you're feeling down, just remember that puzzles can be solved and progressions can be calculated — and don't forget to laugh a little, it's good for the soul!
To find the 10th term of the geometric progression 4, -6, 9, we need to determine the common ratio (r).
The general formula for the nth term of a geometric progression is given by:
an = a1 * r^(n-1)
Where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
In our case, the first term (a1) is 4, and the third term (a3) is 9. We can use these values to find the common ratio:
a3 = a1 * r^(3-1)
9 = 4 * r^2
Dividing both sides by 4, we get:
r^2 = 9/4
Taking the square root of both sides, we have:
r = ±√(9/4)
Since we're dealing with a geometric progression, we assume a positive common ratio. So, we have:
r = √(9/4) = 3/2
Now, we can find the 10th term using the formula:
a10 = a1 * r^(10-1)
a10 = 4 * (3/2)^9
a10 ≈ 4 * 19.683
Calculating the multiplication, we have:
a10 ≈ 78.732
Therefore, the 10th term of the geometric progression 4, -6, 9 is approximately 78.732.
To find the 10th term of a geometric progression with the first term (a) as 4 and the common ratio (r) as -6/4, you can use the formula for the nth term of a geometric progression:
Tn = a * r^(n-1)
In this case, n represents the term number.
Let's substitute the given values into the formula and calculate the 10th term:
T10 = 4 * (-6/4)^(10-1)
= 4 * (-3/2)^9
= 4 * (-19683/512)
= -78732/512
≈ -153.67
Therefore, the 10th term of the geometric progression 4, -6, 9, ... is approximately -153.67.