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nth Term of an AP

The 7th term ...

Question

The 7th term of an AP is -4 and its 13th term is - 16. Find the AP.

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Solution

The nth term of an AP is given by a+(n-1)d.

As per the question, $a + 6 d = - 4 a + 12 d = - 16$

Subtracting we get, $6 d = - 12 \Rightarrow d = - 2$

Now, $a + 6 \times (- 2) = - 4 \Rightarrow a = 8$

So, the AP is 8, 6, 4, 2, 0, -2, -4 .....

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The sum of the first 7 terms of an AP is 182. If its 4th and 17th terms are in teh ratio 1: 5, find the AP.

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