1) The sum of 11 term of an arithmetic progression is 891. Find the 28th and the 45
th if the common difference is 15.
To find the 28th term, we can first find the value of the first term, since we know the common difference and the sum of the first 11 terms.
The sum of an arithmetic progression is given by the formula:
Sum = (n/2)(2a + (n-1)d)
Where n is the number of terms, a is the first term, and d is the common difference.
Plugging in the given values, we have:
891 = (11/2)(2a + (11-1)(15))
Simplifying the equation, we get:
891 = (11/2)(2a + 10(15))
891 = (11/2)(2a + 150)
891 = 11(a + 75)
891 = 11a + 825
11a = 891 - 825
11a = 66
a = 6
So, the first term is 6.
Now, we can use the formula for the nth term of an arithmetic progression:
an = a + (n-1)d
Plugging in the values for the 28th term, we have:
a28 = 6 + (28-1)(15)
a28 = 6 + 27(15)
a28 = 6 + 405
a28 = 411
Therefore, the 28th term is 411.
To find the 45th term, we can plug in the values into the same formula:
a45 = 6 + (45-1)(15)
a45 = 6 + 44(15)
a45 = 6 + 660
a45 = 666
Therefore, the 45th term is 666.