The sum of 11 term of an AP is 891 . Find the 28 & 45 term if common difference is 15
To find the sum of the 11 terms of an arithmetic progression (AP), we can use the formula:
Sum of n terms = (n/2) * (2a + (n-1)d),
where n is the number of terms, a is the first term, and d is the common difference.
In this case, we know that the sum of 11 terms is 891 and the common difference is 15.
891 = (11/2) * (2a + (11-1) * 15)
Expanding the equation, we get:
891 = (11/2) * (2a + 150)
Multiplying both sides by 2, we get:
1782 = 22a + 150
Subtracting 150 from both sides, we get:
1632 = 22a
Dividing both sides by 22, we get:
a = 74.18
Since the first term of an AP cannot be a decimal, we can approximate a to the nearest whole number, which is 74.
Now, we can find the 28th term and the 45th term.
To find any term of an AP, we can use the formula:
Term n = a + (n-1)d,
where Term n is the nth term, a is the first term, and d is the common difference.
28th Term = 74 + (28-1) * 15
= 74 + 27 * 15
= 74 + 405
= 479
45th Term = 74 + (45-1) * 15
= 74 + 44 * 15
= 74 + 660
= 734
Therefore, the 28th term is 479 and the 45th term is 734.