A certain arithmetic progression has a first term of 7 and a common difference o

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Question: A certain arithmetic progression has a first term of 7 and a common difference of 2. What is the sum of the first 10 terms?

Options:

Correct Answer: 75

Solution:

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_10 = 10/2 * (2*7 + 9*2) = 5 * (14 + 18) = 5 * 32 = 160.

A certain arithmetic progression has a first term of 7 and a common difference of 2. What is the sum of the first 10 terms?

A certain arithmetic progression has a first term of 7 and a common difference of 2. What is the sum of the first 10 terms?

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 7.
Step 2: Identify the common difference (d) of the arithmetic progression, which is given as 2.
Step 3: Determine the number of terms (n) we want to sum, which is 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*7 + (10-1)*2).
Step 6: Calculate 10/2, which equals 5.
Step 7: Calculate 2*7, which equals 14.
Step 8: Calculate (10-1)*2, which equals 9*2 = 18.
Step 9: Add 14 and 18 together, which equals 32.
Step 10: Multiply 5 by 32 to get the final sum: 5 * 32 = 160.

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.