The sum to infinity of a g.p is 60. If the first term of the series is 12. Find it's second term
A lot of verbiage there, your solution is hard to read.
S∞ = a/(1-r)
60 = 12/(1-r)
5 = 1/(1-r)
1 = 5 - 5r
5r = 4
r 4/5
term(2) = ar = 12(4/5) = 48/5
Well, let's see. The sum to infinity of a geometric progression (g.p.) can be found using the formula S = a / (1 - r), where S is the sum to infinity, a is the first term, and r is the common ratio.
Given that the sum to infinity is 60 and the first term is 12, we can substitute these values into the formula:
60 = 12 / (1 - r)
Now, let's solve for r:
60(1 - r) = 12
60 - 60r = 12
-60r = 12 - 60
-60r = -48
r = -48 / -60
r = 4/5
To find the second term, we can use the formula for a geometric progression which is a * r^(n-1), where n is the position of the term.
In this case, since we know the first term is 12 (a = 12) and we want to find the second term (n = 2), we can substitute these values into the formula:
second term = 12 * (4/5)^(2-1)
second term = 12 * (4/5)^1
second term = 12 * (4/5)
second term = 48/5
So, the second term of the series is 48/5. But hey, don't worry, I didn't say it was gonna be a whole number! It's just clowning around with fractions here!
To find the second term of a geometric progression (g.p), we need to know the common ratio of the g.p. The common ratio (r) is the ratio between any term and its preceding term in the sequence.
Given that the sum to infinity of the g.p is 60, we can use the formula for the sum of an infinite g.p:
Sum_to_infinity = a / (1 - r)
where a is the first term and r is the common ratio.
We are given that the first term (a) of the g.p is 12, and the sum to infinity is 60. Therefore, we can rewrite the formula as:
60 = 12 / (1 - r)
To solve for r, we can rearrange the equation:
60(1 - r) = 12
60 - 60r = 12
-60r = 12 - 60
-60r = -48
r = (-48) / (-60) = 4/5
Now that we have the common ratio, we can find the second term (a2) using the formula for the nth term of a g.p:
a2 = a * r^(2-1)
Plugging in the values:
a = 12 (the first term)
r = 4/5 (the common ratio)
a2 = 12 * (4/5)^(2-1)
a2 = 12 * (4/5)
a2 = 48/5
Hence, the second term of the g.p is 48/5.
Sum to infinity s=60. First term,a=12. S =a÷1_r=60÷1=12÷1_r. 60(1_r)=12=60_60r=12. 60_12=60r=48÷60=60r÷60. r=48÷60.you reduce into lower term. that is 12 cancel 48 which is equal to 4 and 15 cancel 60 , 5 times. r= 4÷5. Which means that the second term,T2=ar=12×4÷5=48÷5
In a geometric progression (GP), the sum to infinity is given by the formula:
S = a / (1 - r)
Where:
S is the sum to infinity
a is the first term of the series
r is the common ratio
We are given that the sum to infinity is 60 (S = 60) and the first term is 12 (a = 12). We can substitute these values into the formula and solve for the common ratio (r).
60 = 12 / (1 - r)
Now, let's solve for r:
Multiply both sides of the equation by (1 - r):
60(1 - r) = 12
Distribute the 60:
60 - 60r = 12
Subtract 60 from both sides:
-60r = 12 - 60
Simplify:
-60r = -48
Divide both sides by -60:
r = -48 / -60
Simplify:
r = 4 / 5
Now that we have the common ratio (r = 4/5), we can find the second term (a2) using the formula:
a2 = a * r
Given that the first term (a) is 12, we can substitute the values into the formula:
a2 = 12 * (4/5)
Multiply the numbers:
a2 = 48/5
So, the second term of the series is 48/5 or 9.6.