If the first term of an arithmetic progression is 3 and the common difference is

If the first term of an arithmetic progression is 3 and the common difference is 5, what is the sum of the first 6 terms?

If the first term of an arithmetic progression is 3 and the common difference is 5, what is the sum of the first 6 terms?

Step 1: Identify the first term of the arithmetic progression (AP). Here, the first term (a) is 3.
Step 2: Identify the common difference of the AP. Here, the common difference (d) is 5.
Step 3: Determine how many terms we want to sum. In this case, we want to sum the first 6 terms.
Step 4: Use the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 5: Plug in the values into the formula. Here, n = 6, a = 3, and d = 5.
Step 6: Calculate the sum: S_6 = 6/2 * (2*3 + (6-1)*5).
Step 7: Simplify the expression: S_6 = 3 * (6 + 25) = 3 * 31.
Step 8: Calculate the final result: S_6 = 3 * 31 = 93.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.
Sum of an Arithmetic Series – The sum of the first n terms of an arithmetic progression can be calculated using the formula S_n = n/2 * (2a + (n-1)d), where a is the first term, d is the common difference, and n is the number of terms.