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The 6th term and 9th term of an arithmetic progression (AP) are 17 and 26, respectively.

Find:
1. The common difference of the AP.
2. The first term.
3. The 16th term.

Answer :

Final answer:

The common difference of the Arithmetic Progression is 3, the first term is 2, and the 16th term is 47

Explanation:

In Arithmetic Progression(AP), the difference between any two consecutive terms is a constant. This constant is called the common difference of the AP.

We are given that the 6th term is 17 and the 9th term is 26. This implies that in moving from the 6th term to the 9th term (3 steps), the progression has increased by 26-17 = 9. Therefore, the common difference(d) is 9/3 = 3.

To find the first term(a), we use the formula for the nth term which is: a_n = a + (n - 1)*d. Solving it for a (first term) we get a = a_n - (n - 1)*d. Putting n = 6 (because the 6th term is known to us), a_6 =17; and d=3 (which we calculated earlier), we get a = 17 - 5*3 = 2.

To find the 16th term(a_16), from the formula of the nth term, put a=2, d=3, and n=16. We get a_16 = 2 + 15*3 = 47.

So, the common difference of the AP is 3, the first term of the AP is 2, and the 16th term of the AP is 47.

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