the 6 term of a G.P is 2000 its common ratio is 10 find the first term?
a1 = initial value
r = common ratio = 10
The n-th term of a geometric sequence:
an = a1 * r ^ ( n - 1 )
In this case:
a6 = a1 * r ^ 5
2,000 = a1 * 10 ^ 5
2,000 = 100,000 a1 Divide both sides by 100,000
2,000 / 100,000 = a1
0.02 = a1
a1 = 0.02
To find the first term of a geometric progression (G.P), you need to know the specific term and the common ratio.
In this case, you are given:
Term(n) = 6
Common ratio (r) = 10
The formula to find the nth term of a G.P is:
Term(n) = a * r^(n-1)
To find the first term (a), we will substitute the given values into the formula and solve for a.
Term(6) = 2000
2000 = a * 10^(6-1)
2000 = a * 10^5
Divide both sides of the equation by 10^5:
2000 / (10^5) = a
Simplifying the right side:
2000 / 100000 = a
0.02 = a
Therefore, the first term of the G.P is 0.02.