the sum of 11 term of an AP is 891.find the 28th
and 45th term if the common difference is 15
11/2 (2a+10*15) = 891
solve for a, then find
a+27d, a+44d
Why did the arithmetic progression go to a comedy show?
Because it wanted to find some common "difference" to laugh about!
Now, let's solve your question.
We know that the sum of the first 11 terms is 891. Using the formula for the sum of an AP, S = (n/2)(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.
So, we have 891 = (11/2)(2a + 10d). Simplifying this equation, we get 891 = 11a + 55d.
Now, we can solve for the first term (a) using the given common difference (d = 15):
891 = 11a + 55(15)
891 = 11a + 825
11a = 891 - 825
11a = 66
a = 6
Great! Now, we can find the 28th term by substituting the values of a and d into the equation for the nth term of an AP, which is a + (n-1)d:
The 28th term = 6 + (28-1)(15)
The 28th term = 6 + 27(15)
The 28th term = 6 + 405
The 28th term = 411.
Similarly, we can find the 45th term:
The 45th term = 6 + (45-1)(15)
The 45th term = 6 + 44(15)
The 45th term = 6 + 660
The 45th term = 666.
So, the 28th term is 411, and the 45th term is 666.
To find the 28th term of an arithmetic progression (AP) with a common difference of 15, we will use the formula:
An = A1 + (n - 1)d,
where An represents the nth term, A1 is the first term, n is the term number, and d is the common difference.
Given that the sum of the first 11 terms is 891, we can use the formula for the sum of an AP:
Sn = (n/2)(2A1 + (n - 1)d),
where Sn represents the sum of the first n terms.
Substituting the given values into the formulas, we have:
891 = (11/2)(2A1 + (11 - 1)15).
Simplifying:
891 = (11/2)(2A1 + 150).
891 = 11A1 + 825.
11A1 = 891 - 825.
11A1 = 66.
A1 = 66/11.
A1 = 6.
Now that we know the first term (A1 = 6) and the common difference (d = 15), we can find the 28th term:
A28 = A1 + (28 - 1)15.
A28 = 6 + 27 * 15.
A28 = 6 + 405.
A28 = 411.
Therefore, the 28th term of the AP is 411.
To find the 45th term, we can repeat the process:
A45 = A1 + (45 - 1)15.
A45 = 6 + 44 * 15.
A45 = 6 + 660.
A45 = 666.
Therefore, the 45th term of the AP is 666.
To find the sum of an arithmetic progression (AP), you can use the formula:
Sn = (n/2)(2a + (n-1)d)
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
In this case, the sum of 11 terms is given as 891, so we can write the equation as:
891 = (11/2)(2a + (11-1)15)
Let's simplify this equation and solve for a:
891 = (11/2)(2a + 150)
Divide both sides by (11/2):
891 / (11/2) = 2a + 150
Simplifying further:
891 * (2/11) = 2a + 150
162 = 2a + 150
Subtract 150 from both sides:
162 - 150 = 2a
12 = 2a
Divide both sides by 2:
12/2 = a
6 = a
So, the first term (a) of the AP is 6.
Now, we can find the 28th term using the formula:
an = a + (n-1)d
Plugging in the values:
a28 = 6 + (28-1)15
a28 = 6 + 27 * 15
a28 = 6 + 405
a28 = 411
Therefore, the 28th term of the AP is 411.
Similarly, we can find the 45th term using the same formula:
a45 = 6 + (45-1)15
a45 = 6 + 44 * 15
a45 = 6 + 660
a45 = 666
So, the 45th term of the AP is 666.