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

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Question: If the first term of an arithmetic progression is 7 and the common difference is -2, what is the 6th term?

Options:

Correct Answer: -1

Solution:

The nth term is given by a + (n-1)d. Here, a = 7, d = -2, and n = 6. So, the 6th term = 7 + (6-1)(-2) = 7 - 10 = -3.

If the first term of an arithmetic progression is 7 and the common difference is -2, what is the 6th term?

If the first term of an arithmetic progression is 7 and the common difference is -2, what is the 6th term?

Step 1: Identify the first term (a) of the arithmetic progression, which is given as 7.
Step 2: Identify the common difference (d), which is given as -2.
Step 3: Identify the term number (n) we want to find, which is the 6th term, so n = 6.
Step 4: Use the formula for the nth term of an arithmetic progression: nth term = a + (n-1)d.
Step 5: Substitute the values into the formula: 6th term = 7 + (6-1)(-2).
Step 6: Calculate (6-1) which equals 5.
Step 7: Multiply 5 by -2, which equals -10.
Step 8: Add 7 and -10 together: 7 - 10 equals -3.
Step 9: Therefore, the 6th term of the arithmetic progression is -3.

Arithmetic Progression – An arithmetic progression (AP) 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-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.