The sum of 11 term of A.p is 891 .find the 30th term if the common different is 15
To find the 30th term of an arithmetic progression (AP) with a common difference of 15, we can use the formula:
term(n) = term(1) + (n-1) * d
Where term(n) is the nth term, term(1) is the first term, n is the number of terms, and d is the common difference.
Given that the sum of 11 terms is 891, we can use the formula for the sum of an arithmetic progression:
sum(n) = (n/2) * (2*term(1) + (n-1) * d)
Where sum(n) is the sum of the first n terms.
In this case, we can substitute n = 11 and sum(n) = 891 into the sum formula to solve for term(1):
891 = (11/2) * (2*term(1) + (11-1) * 15)
891 = 5.5 * (2*term(1) + 10 * 15)
891 = 5.5 * (2*term(1) + 150)
891 = 5.5 * (2*term(1) + 150)
891 = 11*term(1) + 825
891 - 825 = 11*term(1)
66 = 11*term(1)
66/11 = term(1)
term(1) = 6
Now that we know the first term is 6, we can use the term formula to find the 30th term:
term(30) = 6 + (30-1) * 15
term(30) = 6 + 29 * 15
term(30) = 6 + 435
term(30) = 441
Therefore, the 30th term of the arithmetic progression with a common difference of 15 is 441.
To find the 30th term of an arithmetic progression (AP) given the sum of 11 terms and the common difference, we can follow these steps:
Step 1: Find the sum of the 11 terms using the formula for the sum of an AP:
- Sum of AP = (n/2) * (2a + (n-1)d)
where n is the number of terms, a is the first term, and d is the common difference.
- Given n = 11, Sum of 11 terms = 891, and d = 15:
891 = (11/2) * (2a + (11-1)*15)
891 = 11 * (2a + 10*15)
891 = 11 * (2a + 150)
891 = 22a + 1650
22a = 891 - 1650
22a = -759
- Divide both sides by 22:
a = -759/22
a ≈ -34.5 (approximately)
Step 2: Find the 30th term of the AP:
- We can use the formula for the nth term of an AP:
- nth term = a + (n-1)d
where n is the term number, a is the first term, and d is the common difference.
- Given n = 30 and d = 15:
30th term = -34.5 + (30-1)*15
30th term = -34.5 + 29*15
30th term = -34.5 + 435
30th term = 400.5
Therefore, the 30th term of the arithmetic progression is 400.5.
To find the 30th term of an arithmetic progression (A.P.) with a sum of 891 and a common difference of 15, we can use the formula for the sum of an A.P. and solve for the term to be found. Here's how you can do it step-by-step:
Step 1: Write down the information given:
- Sum of 11 terms (S11) = 891
- Common difference (d) = 15
Step 2: Use the formula for the sum of an A.P. to find the 11th term (a11):
S11 = (11/2)[2a1 + (11-1)d]
891 = (11/2)[2a1 + 10(15)]
891 = (11/2)[2a1 + 150]
Divide both sides of the equation by 11/2:
891 / (11/2) = 2a1 + 150
891 * (2/11) = 2a1 + 150
162 = 2a1 + 150
2a1 = 162 - 150
2a1 = 12
Divide both sides of the equation by 2:
a1 = 12/2
a1 = 6
Step 3: Use the formula for the nth term of an A.P. to find the 30th term (a30) with the known values of a1 and d:
a30 = a1 + (n - 1)d
a30 = 6 + (30 - 1)15
a30 = 6 + 29 * 15
a30 = 6 + 435
a30 = 441
Therefore, the 30th term of the given A.P. with a common difference of 15 is 441.