If the first term of an arithmetic progression is 12 and the last term is 48, wi

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Question: If the first term of an arithmetic progression is 12 and the last term is 48, with a total of 10 terms, what is the common difference?

Options:

Correct Answer: 4

Solution:

The last term can be expressed as a + (n-1)d. Here, 48 = 12 + 9d. Solving gives d = 4.

If the first term of an arithmetic progression is 12 and the last term is 48, with a total of 10 terms, what is the common difference?

If the first term of an arithmetic progression is 12 and the last term is 48, with a total of 10 terms, what is the common difference?

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 12.
Step 2: Identify the last term of the arithmetic progression, which is given as 48.
Step 3: Identify the total number of terms (n), which is given as 10.
Step 4: Use the formula for the last term of an arithmetic progression: last term = first term + (number of terms - 1) * common difference.
Step 5: Substitute the known values into the formula: 48 = 12 + (10 - 1) * d.
Step 6: Simplify the equation: 48 = 12 + 9d.
Step 7: Subtract 12 from both sides: 48 - 12 = 9d, which simplifies to 36 = 9d.
Step 8: Divide both sides by 9 to find the common difference (d): d = 36 / 9.
Step 9: Calculate the value: d = 4.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Formula for the nth term – The nth term of an arithmetic progression can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.