What is the sum of the first 15 terms of an arithmetic progression where the fir

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Question: What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?

Options:

Correct Answer: 120

Solution:

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.

What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?

What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?

Step 1: Identify the first term (a) and the common difference (d) of the arithmetic progression. Here, a = 2 and d = 4.
Step 2: Determine the number of terms (n) you want to sum. In this case, n = 15.
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_15 = 15/2 * (2*2 + (15-1)*4).
Step 5: Calculate 2*2, which equals 4.
Step 6: Calculate (15-1)*4, which equals 14*4 = 56.
Step 7: Add the results from Step 5 and Step 6: 4 + 56 = 60.
Step 8: Now substitute back into the formula: S_15 = 15/2 * 60.
Step 9: Calculate 15/2, which equals 7.5.
Step 10: Finally, multiply 7.5 by 60 to get the sum: 7.5 * 60 = 450.

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