In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what

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Question: In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?

Options:

Correct Answer: 6

Solution:

Let the common difference be d. From the equations 4 + 5d = 24, solving gives d = 4.

In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?

In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?

Step 1: Identify the first term of the arithmetic progression, which is given as 4.
Step 2: Identify the sixth term of the arithmetic progression, which is given as 24.
Step 3: Recall the formula for the nth term of an arithmetic progression: nth term = first term + (n-1) * common difference.
Step 4: For the sixth term (n=6), the formula becomes: 6th term = 4 + (6-1) * d.
Step 5: Substitute the known values into the equation: 24 = 4 + 5d.
Step 6: Simplify the equation: 24 - 4 = 5d, which gives 20 = 5d.
Step 7: Solve for d by dividing both sides by 5: d = 20 / 5.
Step 8: 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.
Common Difference – The common difference in an AP is the fixed amount added to each term to get the next term.
Term Calculation – The nth term of an AP can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.