Question

Determine the nth term of the AP whose 7th term is - 1 and 16th term is 17.

Answer 1

Here is your answer.

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Answer 2

We know that nth term of an AP is an = a + (n - 1) * d

(i)

Given that 7th term of an AP is -1.

⇒ a7 = a + (7 - 1) * d

⇒ -1 = a + 6d    ------ (1)

(ii)

Given that 16th term of AP is 17.

⇒ a16 = a + (16 - 1) * d

⇒ 17 = a + 15d     ------ (2)

On solving (1) & (2), we get

⇒ a + 6d = -1

⇒ a + 15d = 17

    -----------------

          -9d = -18

              d = 2.

Substitute d = 2 in (1), we get

⇒ a + 6d = -1

⇒ a + 6(2) = -1

⇒ a + 12 = -1

⇒ a = -13.

Now,

⇒ nth term of the AP an = a + (n - 1) * d

                                         = -13 + (n - 1) * 2

                                         = -13 + 2n - 2

                                         = 2n - 15.

Therefore, nth term of the AP = 2n - 15.

Hope this helps!