If the 1st term of an arithmetic progression is 4 and the common difference is 3

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Question: If the 1st term of an arithmetic progression is 4 and the common difference is 3, what is the sum of the first 10 terms?

Options:

Correct Answer: 80

Solution:

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_10 = 10/2 * (2*4 + 9*3) = 5 * (8 + 27) = 5 * 35 = 175.

If the 1st term of an arithmetic progression is 4 and the common difference is 3, what is the sum of the first 10 terms?

If the 1st term of an arithmetic progression is 4 and the common difference is 3, what is the sum of the first 10 terms?

Step 1: Identify the first term (a) of the arithmetic progression. Here, a = 4.
Step 2: Identify the common difference (d) of the arithmetic progression. Here, d = 3.
Step 3: Determine the number of terms (n) you want to sum. Here, n = 10.
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: Substitute the values into the formula: S_10 = 10/2 * (2*4 + (10-1)*3).
Step 6: Calculate 10/2, which equals 5.
Step 7: Calculate 2*4, which equals 8.
Step 8: Calculate (10-1)*3, which equals 9*3 = 27.
Step 9: Add the results from Step 7 and Step 8: 8 + 27 = 35.
Step 10: Multiply the result from Step 6 by the result from Step 9: 5 * 35 = 175.

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