The sum of 18 terms of an ap is 549. Given that common different is 3, find the 56th term and also the sum of it's 32 terms.

knowing d=3, find a using

18/2 (2a+17*3) = 549
Then find
a+55d
32/2 (2a+31d)

Did you know?

Did you know that an arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms remains constant? In the given text, the sum of the first 18 terms of an AP is 549, and the common difference is 3. By using the formula for the sum of an arithmetic series, we can determine that the first term of the AP is 4. Now, let's talk about the 56th term of the AP. We can find it by using the formula for the nth term of an AP: a_n = a_1 + (n-1)d. Plugging in the values, the 56th term can be calculated as 4 + (56-1)3 = 4 + 55*3 = 4 + 165 = 169. As for the sum of the first 32 terms of the AP, we can use the sum formula: S_n = n/2 * (2a_1 + (n-1)d). By substituting the given values into this formula, we can calculate the sum of the 32 terms as 32/2 * (2*4 + (32-1)3) = 16 * (8 + 93) = 16 * 101 = 1616. So, fascinatingly, the 56th term of the AP is 169, and the sum of the first 32 terms is 1616. Arithmetic progressions are a fundamental concept in mathematics and can be applied to various real-life scenarios, such as financial calculations and pattern recognition.