The sum of 11terms of an a.pis 891.find the 28 and 45 terms of the common difference is 15
Let's call the first term of the arithmetic progression "a" and the common difference "d".
We are given that the sum of 11 terms of the arithmetic progression is 891.
The sum of an arithmetic progression can be calculated using the formula: 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.
Plugging in the given values, we get: 891 = (11/2)(2a + 10d) [equation 1]
We are also given that the common difference is 15.
The 28th term can be calculated using the formula: a + (n-1)d, where n is the term number.
Plugging in n = 28 and d = 15, we get: 28th term = a + 15(28-1) = a + 405 [equation 2]
Similarly, the 45th term can be calculated using the formula: a + (n-1)d.
Plugging in n = 45 and d = 15, we get: 45th term = a + 15(45-1) = a + 660 [equation 3]
To find the values of 'a' and 'd', we need to solve equations 1, 2, and 3 simultaneously.
From equation 2, we have a + 405 = 28th term. Rearranging, we get: a = 28th term - 405 [equation 4]
From equation 3, we have a + 660 = 45th term. Rearranging, we get: a = 45th term - 660 [equation 5]
Equating equations 4 and 5, we get: 28th term - 405 = 45th term - 660
Rearranging, we get: 28th term - 45th term = -660 + 405
Simplifying, we get: -17th term = -255
Dividing by -17, we get: 28th term - 45th term = 15
So, the 28th and 45th terms have a difference of 15.