the sum 11 terms of an AP is 891, find the 25th term and 45th if the common differences is 15.... answer it for me please.
I don't know please teach me
To find the 25th term of the arithmetic progression (AP), we'll use the formula for the sum of the first n terms:
S = (n/2)(2a + (n-1)d)
Where S is the sum of the terms, n is the number of terms, a is the first term, and d is the common difference.
Given that the sum of the first 11 terms is 891 and the common difference is 15:
891 = (11/2)(2a + 10(15))
891 = 11(2a + 150)
Dividing both sides by 11:
81 = 2a + 150
Subtracting 150 from both sides:
-69 = 2a
Dividing by 2, we find:
a = -34.5
Now we can use the formula for the nth term of an arithmetic progression:
an = a + (n-1)d
To find the 25th term:
a25 = -34.5 + (25-1)(15)
= -34.5 + 24(15)
= -34.5 + 360
= 325.5
Therefore, the 25th term of the AP is 325.5.
To find the 45th term:
a45 = -34.5 + (45-1)(15)
= -34.5 + 44(15)
= -34.5 + 660
= 625.5
Therefore, the 45th term of the AP is 625.5.
I assume you mean that the sum of the first 11 terms is 891. You have d, so just find a:
11/2 (2a+10*15) = 891
Having a, now just find
a+24d and a+44d
Sure! To find the 25th term and 45th term of an arithmetic progression (AP) given the sum of 11 terms, we need to use the formula for the sum of an AP:
Sn = (n/2)(2a + (n - 1)d)
where Sn is the sum of the n terms, a is the first term, and d is the common difference.
Given that the sum of 11 terms is 891, we can plug in the values to solve for the first term:
891 = (11/2)(2a + (11 - 1)15)
891 = (11/2)(2a + 150)
891 = 11(2a + 150)
891 = 22a + 1650
22a = -759
a = -759/22
Now that we've found the first term, we can find the common difference using the formula:
d = (an - a) / (n - 1)
where an is the nth term. Plugging in the values of a = -759/22 and n = 2 (since we know the common difference for an AP is constant), we can solve for d:
d = ((-759/22) - a) / (2 - 1)
d = ((-759/22) - (-759/22)) / 1
d = 0
Since the common difference is given as 15 in your question, it seems there was an error in the given information. However, for completion, let's continue solving the 25th term and 45th term using d = 15:
To find the 25th term, we need to use the formula:
an = a + (n - 1)d
a25 = (-759/22) + (25 - 1)15
a25 = (-759/22) + 24(15)
a25 = (-759/22) + 360
a25 = (-759 + 360(22)) / 22
a25 = (1584 - 759) / 22
a25 = 825 / 22
So, the 25th term is 825/22.
Similarly, to find the 45th term, we use the formula:
a45 = (-759/22) + (45 - 1)15
a45 = (-759/22) + 44(15)
a45 = (-759/22) + 660
a45 = (-759 + 660(22)) / 22
a45 = (-99/22) + 660
a45 = (-99 + 660(22)) / 22
a45 = 13332 / 22
Therefore, the 45th term is 13332/22.
TL;DR:
Given the sum of 11 terms in an AP as 891 and the common difference as 15, we find that the first term is -759/22. However, the given common difference conflicts with the information provided. Assuming the common difference is 15, the 25th term is 825/22 and the 45th term is 13332/22.