How many terms of the series 5 + 7 + 9 must be taken so that sum may be 480? Please answer in short
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.
What will 6 ^ (th) term of the series 1 + 3+9?
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.
AAAaannndd the bot gets it wrong yet again!
a=5, d=2, so
n/2 (2*5 + 2(n-1)) = 480
n=20
You are correct and I apologize for my mistake. The correct answer is indeed n=20. Thank you for correcting me.
To find out how many terms of the series 5 + 7 + 9 must be taken to get a sum of 480, we can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is given by: Sn = n/2 * (2a + (n-1)d)
Here, Sn represents the sum of the series, n represents the number of terms in the series, a represents the first term in the series, and d represents the common difference.
In this case, the first term (a) is 5 and the common difference (d) is 2. We want the sum (Sn) to be 480.
So, we can set up the equation: 480 = n/2 * (2*5 + (n-1)*2)
Simplifying this equation, we get: 480 = n/2 * (10 + 2n - 2)
Further simplifying, we have: 480 = n/2 * (8 + 2n)
Now, we can solve this equation to find the value of n.
To find the number of terms required, we need to determine how many terms of the series 5, 7, 9 add up to a sum of 480.
Let's start by determining the common difference between the terms. In this series, the common difference is obtained by subtracting the first term (5) from the second term (7), which gives us 2.
Next, we need to find the nth term formula (or the general term formula) of the series, which is given by:
an = a1 + (n-1)d
Where:
an represents the nth term,
a1 represents the first term, and
d represents the common difference.
Now, we can set up the equation to find the number of terms (n):
5 + (n-1)2 = 480
Simplifying the equation:
5 + 2n - 2 = 480
2n + 3 = 480
2n = 477
n = 477/2
n ≈ 238.5
Since we can't have a fraction for the number of terms, we need to round it up to the nearest whole number. Therefore, we would need to take 239 terms of the series 5, 7, 9 in order to obtain a sum of 480.