Question
How many terms of the series 5 + 7 + 9 must be taken so that sum may be 480? Please answer in short
Answers
Bot
To solve this problem, we need to use the formula for the sum of an arithmetic series:
S = n/2[2a + (n-1)d]
Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, we have:
a = 5
d = 7 - 5 = 2
S = 480
Substituting these values into the formula, we get:
480 = n/2[2(5) + (n-1)(2)]
Simplifying:
480 = n/2[10 + 2n - 2]
480 = n/2[8 + 2n]
960 = n(4 + n)
Rearranging and solving for n, we get:
n^2 + 4n - 960 = 0
Using the quadratic formula:
n = (-4 ± sqrt(4^2 - 4(1)(-960)))/2(1)
n = (-4 ± sqrt(3856))/2
n ≈ 19.56 or n ≈ -23.56
Since we can't have a negative number of terms, we need to round up to the nearest integer. Therefore, we need to take 20 terms of the series in order for the sum to be 480.
S = n/2[2a + (n-1)d]
Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, we have:
a = 5
d = 7 - 5 = 2
S = 480
Substituting these values into the formula, we get:
480 = n/2[2(5) + (n-1)(2)]
Simplifying:
480 = n/2[10 + 2n - 2]
480 = n/2[8 + 2n]
960 = n(4 + n)
Rearranging and solving for n, we get:
n^2 + 4n - 960 = 0
Using the quadratic formula:
n = (-4 ± sqrt(4^2 - 4(1)(-960)))/2(1)
n = (-4 ± sqrt(3856))/2
n ≈ 19.56 or n ≈ -23.56
Since we can't have a negative number of terms, we need to round up to the nearest integer. Therefore, we need to take 20 terms of the series in order for the sum to be 480.
Bipana
What will 6 ^ (th) term of the series 1 + 3+9?
Bot
The given series is 1 + 3 + 9.
This is a geometric series with a common ratio of 3.
We can find the 6th term of the series using the formula for the nth term of a geometric series:
an = a1 * r^(n-1)
where an is the nth term of the series, a1 is the first term, r is the common ratio, and n is the number of the term we want to find.
In this case, we have:
a1 = 1
r = 3
n = 6
Substituting these values into the formula, we get:
a6 = 1 * 3^(6-1)
a6 = 1 * 3^5
a6 = 1 * 243
a6 = 243
Therefore, the 6th term of the series 1 + 3 + 9 is 243.
This is a geometric series with a common ratio of 3.
We can find the 6th term of the series using the formula for the nth term of a geometric series:
an = a1 * r^(n-1)
where an is the nth term of the series, a1 is the first term, r is the common ratio, and n is the number of the term we want to find.
In this case, we have:
a1 = 1
r = 3
n = 6
Substituting these values into the formula, we get:
a6 = 1 * 3^(6-1)
a6 = 1 * 3^5
a6 = 1 * 243
a6 = 243
Therefore, the 6th term of the series 1 + 3 + 9 is 243.
oobleck
AAAaannndd the bot gets it wrong yet again!
a=5, d=2, so
n/2 (2*5 + 2(n-1)) = 480
n=20
a=5, d=2, so
n/2 (2*5 + 2(n-1)) = 480
n=20
Bot
You are correct and I apologize for my mistake. The correct answer is indeed n=20. Thank you for correcting me.