the first and seven term of a G.P are 40½ and 1/18 respectively. find the second term
a = 40.5 = 81/2
a r^6 = 1/18
r^6 = (1/18)(2/81) = 2 / (2*9 *9 *9 ) = 1/3^6
so
r = 1/3
second term is a r = (81/2)(1/3) = 81/6 = 27/2
What does the astheric mean
I don't know
Well, let's start by making a big "G" out of play-dough, and then we can put a little "P" on top. Voila, we have a G.P.! Now, to find the second term, we need to activate our math mode.
In a geometric progression (G.P.), each term is found by multiplying the previous term by a common ratio. So, let's divide the seventh term (1/18) by the first term (40½) to find the common ratio.
(1/18) / (40½) = 1/18 * 2/81 = 2/1458
Now, to find the second term, we just need to multiply the first term (40½) by the common ratio (2/1458).
40½ * 2/1458 = 81/2 * 2/1458 = 81/1458 ≈ 0.0558
So, the second term of the G.P. is approximately 0.0558. But remember, numbers are just like jokes – they can sometimes be a little tricky, so double-check your calculations just to be sure!
To find the second term of a geometric progression (G.P.), we need to determine the common ratio (r) first.
The formula for the nth term (aₙ) of a G.P. is given by:
aₙ = a₁ * r^(n-1),
where a₁ is the first term and r is the common ratio.
Given that the first term (a₁) is 40½ (or 81/2) and the seventh term (a₇) is 1/18, we can use these values to calculate r, the common ratio.
Using the formula for the terms, we have:
a₁ = 81/2
a₇ = a₁ * r^(7-1)
= a₁ * r^6
Substituting the given values:
1/18 = 81/2 * r^6
To solve for r, we can simplify and solve the resulting equation:
1/18 = (81/2) * r^6
Multiply both sides by 2 to eliminate the fraction:
2/18 = 81 * r^6
Simplify the left side:
1/9 = 81 * r^6
Divide both sides by 81:
1/9 * 1/81 = r^6
1/729 = r^6
Take the sixth root of both sides:
(r^6)^(1/6) = (1/729)^(1/6)
r = 1/9
Now that we have the common ratio (r = 1/9), we can find the second term (a₂) using the formula for the terms:
a₂ = a₁ * r^(2-1)
= a₁ * r
Substituting the values:
a₂ = 81/2 * (1/9)
= (81/2) / 9
= 9/2
Therefore, the second term of the geometric progression is 9/2.