If the first term of an arithmetic progression is 8 and the last term is 50, wit

If the first term of an arithmetic progression is 8 and the last term is 50, with a total of 10 terms, what is the common difference? (2023)

If the first term of an arithmetic progression is 8 and the last term is 50, with a total of 10 terms, what is the common difference? (2023)

Step 1: Identify the first term of the arithmetic progression (AP), which is given as 8.
Step 2: Identify the last term of the AP, which is given as 50.
Step 3: Identify the total number of terms in the AP, which is given as 10.
Step 4: Use the formula for the nth term of an AP: nth term = first term + (n-1) * common difference.
Step 5: Substitute the known values into the formula: 50 = 8 + (10-1)d.
Step 6: Simplify the equation: 50 = 8 + 9d.
Step 7: Subtract 8 from both sides: 50 - 8 = 9d, which simplifies to 42 = 9d.
Step 8: Divide both sides by 9 to solve for d: d = 42 / 9.
Step 9: Simplify the fraction: d = 4.67 (approximately) or d = 5 when rounded.

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, d is the common difference, and n is the term number.