If the 7th term of an arithmetic progression is 25 and the common difference is

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Question: If the 7th term of an arithmetic progression is 25 and the common difference is 3, what is the 1st term?

Options:

Correct Answer: 10

Solution:

Using the formula for the nth term, a + 6d = 25. Substituting d = 3 gives a + 18 = 25, thus a = 7.

If the 7th term of an arithmetic progression is 25 and the common difference is 3, what is the 1st term?

If the 7th term of an arithmetic progression is 25 and the common difference is 3, what is the 1st 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: Since we need the 7th term, we set n = 7 in the formula: 7th term = a + (7-1)d.
Step 4: Simplify the formula: 7th term = a + 6d.
Step 5: We know the 7th term is 25, so we can write the equation: a + 6d = 25.
Step 6: Substitute the value of the common difference (d = 3) into the equation: a + 6(3) = 25.
Step 7: Calculate 6 times 3: 6(3) = 18, so the equation becomes: a + 18 = 25.
Step 8: To find the first term (a), subtract 18 from both sides: a = 25 - 18.
Step 9: Calculate the result: a = 7.

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.