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

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.