In an arithmetic progression, if the first term is 12 and the last term is 48, a

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Question: In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 10 terms, what is the common difference?

Options:

Correct Answer: 4

Solution:

Using the formula for the last term, 48 = 12 + (10-1)d. Solving gives d = 4.

In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 10 terms, what is the common difference?

In an arithmetic progression, if the first term is 12 and the last term is 48, and there are 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 (l) of the arithmetic progression, which is given as 48.
Step 3: Identify the number of terms (n) in the arithmetic progression, which is given as 10.
Step 4: Use the formula for the last term of an arithmetic progression: l = a + (n - 1)d.
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 d: d = 36 / 9.
Step 9: Calculate the value of d: 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 = a + (n-1)d, where a is the first term, n is the number of terms, and d is the common difference.