The sum of 11terms of an Ap is 891 find the 28th and 45th terms if the common difference is 15
To find the 28th and 45th terms of an arithmetic progression (AP), we need to know the first term (a) and the common difference (d).
Given that the common difference (d) is 15, we can use this information to find the first term (a) by working backwards.
Step 1: Let's calculate the sum of the first 11 terms of the AP. The sum of an AP can be determined using the formula:
Sn = n/2 * [2a + (n-1)d],
where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Given that the sum (Sn) of the first 11 terms is 891, we can substitute the given values into the formula:
891 = 11/2 * [2a + (11-1)15].
Step 2: Simplify the equation:
891 = 11/2 * [2a + 10 * 15].
891 = 11/2 * [2a + 150].
891 = 11/2 * (2a + 150).
891 = 11a + 11 * 75.
891 = 11a + 825.
891 - 825 = 11a.
66 = 11a.
Step 3: Solve for a:
Divide both sides of the equation by 11:
66/11 = a.
a = 6.
So, we have found that the first term (a) is 6.
Step 4: Now that we know the first term (a) and the common difference (d), we can find the 28th and 45th terms of the AP.
For the 28th term, we can use the formula:
An = a + (n-1)d.
Substituting the values:
A28 = 6 + (28-1) * 15.
A28 = 6 + 27 * 15.
A28 = 6 + 405.
A28 = 411.
Therefore, the 28th term of the AP is 411.
For the 45th term, we can use the same formula:
A45 = 6 + (45-1) * 15.
A45 = 6 + 44 * 15.
A45 = 6 + 660.
A45 = 666.
Hence, the 45th term of the AP is 666.
assuming you mean the sum of the first 11 terms is 891, you have
11/2 (2a + 10*15) = 891
Having a, you want
a+27d
a+44d