The sum of 18terms of an A.P is 549.given that the common difference is 3. find the 56th term
18/2 (2a+17d) = 549
Now plug in d and find a, and then you want
T56 = a+55d
Tnxs guys
To find the 56th term of an arithmetic progression (AP), we need to know the first term, the common difference, and the formula to find the nth term of an AP.
In this case, the common difference is given as 3. However, we are not given the first term of the AP. Therefore, we need to find the first term of the AP based on the sum of the first 18 terms.
The formula to find the sum of the first n terms of an AP is: Sn = (n/2)(2a + (n-1)d), where Sn represents the sum, n is the number of terms, a is the first term, and d is the common difference.
Using the given information, the sum of the first 18 terms is 549, and the common difference is 3. We can substitute these values into the formula and solve for the first term, a.
549 = (18/2)(2a + (18-1)(3))
549 = 9(2a + 51)
Divide both sides of the equation by 9:
61 = 2a + 51
Subtract 51 from both sides of the equation:
10 = 2a
Divide both sides of the equation by 2:
a = 5
Now that we have found the first term of the AP as 5, we can use the formula for the nth term of an AP to find the 56th term.
The formula to find the nth term of an AP is: an = a + (n-1)d, where an is the nth term, a is the first term, n is the term number, and d is the common difference.
Substituting the values into the formula, we have:
a56 = 5 + (56-1)(3)
a56 = 5 + 55(3)
a56 = 5 + 165
a56 = 170
Therefore, the 56th term of the AP is 170.