In an arithmetic progression, if the first term is 10 and the common difference

In an arithmetic progression, if the first term is 10 and the common difference is 5, what is the sum of the first 8 terms?

In an arithmetic progression, if the first term is 10 and the common difference is 5, what is the sum of the first 8 terms?

Step 1: Identify the first term (a) and the common difference (d) of the arithmetic progression. Here, a = 10 and d = 5.
Step 2: Determine how many terms (n) you want to sum. In this case, n = 8.
Step 3: Use the formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).
Step 4: Substitute the values into the formula: S_8 = 8/2 * (2*10 + (8-1)*5).
Step 5: Calculate 2*10, which equals 20.
Step 6: Calculate (8-1)*5, which equals 7*5 = 35.
Step 7: Add the results from Step 5 and Step 6: 20 + 35 = 55.
Step 8: Now calculate 8/2, which equals 4.
Step 9: Finally, multiply 4 by 55 to get the sum: 4 * 55 = 220.

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