The sum of 18nth terms of an ap is 549.given that the common difference is 3
Find the 56th term and also the sum of its 32 term
Using the formula for the sum of the terms of an arithmetic progression, we have:
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, and n is the number of terms.
Given that the common difference is 3, we can substitute the known values into the formula:
549 = (18/2)(2a + (18-1)3)
549 = 9(2a + 17*3)
549 = 9(2a + 51)
549 = 18a + 459
18a = 549 - 459
18a = 90
a = 90/18
a = 5
Therefore, the first term of the arithmetic progression is 5.
To find the 56th term, we can use the formula:
aₙ = a + (n-1)d
a₅₆ = 5 + (56-1)3
a₅₆ = 5 + 55*3
a₅₆ = 5 + 165
a₅₆ = 170
Therefore, the 56th term of the arithmetic progression is 170.
To find the sum of the 32 terms, we can use the formula:
Sₙ = (n/2)(2a + (n-1)d)
S₃₂ = (32/2)(2*5 + (32-1)3)
S₃₂ = 16(10 + 31*3)
S₃₂ = 16(10 + 93)
S₃₂ = 16(103)
S₃₂ = 1648
Therefore, the sum of the 32 terms is 1648.