If the 7th term of an arithmetic progression is 50 and the common difference is

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Question: If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?

Options:

Correct Answer: 30

Solution:

Using the formula for the nth term, a + 6d = 50. Substituting d = 5 gives a + 30 = 50, hence a = 20.

If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?

If the 7th term of an arithmetic progression is 50 and the common difference is 5, what is the first term?

Step 1: Understand that an arithmetic progression (AP) has a first term (a) and a common difference (d).
Step 2: The formula for the nth term of an AP is given by: nth term = a + (n-1)d.
Step 3: Identify that the 7th term is given as 50, so we set n = 7.
Step 4: Substitute n = 7 into the formula: 7th term = a + (7-1)d.
Step 5: Simplify the equation: 7th term = a + 6d.
Step 6: Substitute the known values into the equation: a + 6 * 5 = 50.
Step 7: Calculate 6 * 5, which equals 30, so the equation becomes: a + 30 = 50.
Step 8: To find the first term (a), subtract 30 from both sides: a = 50 - 30.
Step 9: Calculate the result: a = 20.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.
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.