In an arithmetic progression, if the first term is 4 and the last term is 40, an

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Question: In an arithmetic progression, if the first term is 4 and the last term is 40, and there are 10 terms, what is the common difference?

Options:

Correct Answer: 5

Solution:

Using the nth term formula, we have 40 = 4 + (10-1)d. Solving gives d = 4.

In an arithmetic progression, if the first term is 4 and the last term is 40, and there are 10 terms, what is the common difference?

In an arithmetic progression, if the first term is 4 and the last term is 40, 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 4.
Step 2: Identify the last term (l) of the arithmetic progression, which is given as 40.
Step 3: Identify the number of terms (n) in the arithmetic progression, which is given as 10.
Step 4: Use the formula for the nth term of an arithmetic progression: l = a + (n-1)d.
Step 5: Substitute the known values into the formula: 40 = 4 + (10-1)d.
Step 6: Simplify the equation: 40 = 4 + 9d.
Step 7: Subtract 4 from both sides: 40 - 4 = 9d, which gives 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.
Nth Term Formula – 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.