The sum of 10term of an AP is 891, find the 28th and 45th term if the common difference is 14
S10 = 10/2 (2a + 9d) = 891
You have d=14, so use the above equation to find a.
Then just find a+27d and a+44d
To find the sum of the first 10 terms 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
d is the common difference
n is the number of terms
Given that the sum of the first 10 terms is 891 and the common difference is 14, we can substitute these values into the formula and solve for the first term (a).
891 = (10/2)[2a + (10-1)14]
891 = 5[2a + 9 * 14]
891 = 5[2a + 126]
891 = 10a + 630
261 = 10a
a = 261/10
a = 26.1
Now that we have the first term (a), we can find the 28th and 45th terms using the formula for the nth term of an arithmetic progression:
an = a + (n-1)d
Substituting the values, we get:
a28 = 26.1 + (28-1)14
a28 = 26.1 + 27 * 14
a28 = 26.1 + 378
a28 = 404.1
a45 = 26.1 + (45-1)14
a45 = 26.1 + 44 * 14
a45 = 26.1 + 616
a45 = 642.1
Therefore, the 28th term is 404.1 and the 45th term is 642.1.