Question

the third term of an ap is p & the 4 th term is q find the 10 th term​

Answer 1

Step-by-step explanation:

Given that,

third term of an A.P. is p

and 4th term is q

Therefore,

Common difference(d) = 4th term - 3rd term

                                     d = q - p

Let first term of the A.P. be a

∴ 3rd term = a + 2d     [∵ nth term = a + (n - 1)d]

⇒p = a + 2(q - p)

⇒3p - 2q = a

∴ 10th term = a + 9d       [∵ nth term = a + (n - 1)d]

                   = (3p - 2q) + 9(q - p)   [∵ a = (3p - 2q) & d = (q - p)]

                    = 3p - 2q + 9q - 9p

                    = 7q - 6p

∴ 10th term is (7q - 6p)

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