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The 3rd and 8th term of an arithmetic progression is -13 and 2 respectively. What is the 14th term?

The 3rd and 8th term of an arithmetic progression is -13 and 2 respectively. What is the 14th term? Correct Answer 20

If a is the first term and d is the common difference then the third term of the AP is given by

a + 2d = -13      ----(1)

And 8th term is given by

a + 7d = 2      ----(2)

Subject (1) from (2)

5d = 15

⇒ d = 3

Put in equation (1)

a = -13 - 6 = -19

14th term will be given as

a + 13d = -19 + 13 × 3 = -19 + 39 = 20

∴ The 14th term = 20

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