the 6 term of a G.P is 2000 its common ratio is 10 find the first term?
To find the first term (a) of a geometric progression (G.P) when given the 6th term (t6) and the common ratio (r), we can use the formula:
t6 = a * (r^(6-1))
Given t6 = 2000 and r = 10, we can substitute these values into the formula and solve for a.
2000 = a * (10^(6-1))
Simplifying,
2000 = a * (10^5)
To find 10^5, we know that any number raised to the power of 0 is equal to 1, and 10 raised to the power of 1 is 10. So, 10^5 will be equal to 10 * 10 * 10 * 10 * 10 = 100,000.
Now, our equation becomes:
2000 = a * 100,000
To isolate a, we can divide both sides of the equation by 100,000:
2000 / 100,000 = a
Simplifying,
0.02 = a
Therefore, the first term (a) of the geometric progression is 0.02.
To find the first term of a geometric progression (G.P.), you need to know the common ratio and one of the terms. In this case, you know that the 6th term of the G.P. is 2000 and the common ratio is 10.
You can use the formula for the nth term of a G.P. to find the first term. The formula is:
an = a1 * r^(n-1)
Where:
an is the nth term
a1 is the first term
r is the common ratio
n is the term number
Now, let's use the given information to find the first term:
Using the formula:
2000 = a1 * 10^(6-1)
Simplifying the equation:
2000 = a1 * 10^5
Dividing both sides by 10^5:
2000 / 10^5 = a1
Simplifying further:
0.02 = a1
Therefore, the first term of the geometric progression is 0.02.