The the sum of the 11th term of an AP is 891 find the 28 and the 45th term if the common difference is 15
To find the 11th term of an arithmetic progression, we can use the formula:
An = A1 + (n-1)d
where An is 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 11th term is 891, we can determine the 11th term:
891 = 11/2 * (2A1 + (11-1)d)
891 = 11/2 * (2A1 + 10d)
891 = 11 * (A1 + 5d)
Now, we know that the common difference, d, is 15. So we can substitute this into the equation:
891 = 11 * (A1 + 5*15)
891 = 11 * (A1 + 75)
891 = 11A1 + 825
66 = 11A1
A1 = 6
Now that we have found the first term, A1, we can find the 28th term:
A28 = A1 + (28-1)d
A28 = 6 + 27*15
A28 = 6 + 405
A28 = 411
Similarly, we can find the 45th term:
A45 = A1 + (45-1)d
A45 = 6 + 44*15
A45 = 6 + 660
A45 = 666
Therefore, the 28th term is 411 and the 45th term is 666.