Question

The sum of 11 term of an AP is 891 . Find the 28 & 45 term if common difference is 15

Answer 1

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.