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

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Question: 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?

Options:

Correct Answer: 140

Solution:

The sum of the first n terms is given by S_n = n/2 * (2a + (n-1)d). Here, S_8 = 8/2 * (20 + 35) = 4 * 55 = 220.

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.

Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
Sum of Terms Formula – The formula for the sum of the first n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d).