The first three terms of an arithmetic sequence are p, 6 and 2p-3. What is the tenth term of this sequence?

a1 = p a2 = 6 a3 = 2p - 3

Number of terms = n = 10

Now difference = d = a2 - a1 = 6 - p

Now the tenth term is

a10 = a1 + (n - 1)d

a10 = p + (10 - 1)(6 - p)

a10 = p + (9)(6 - p)

a10 = p + (54 - 9p)

a10 = p + 54 - 9p

a10 = 54 - 8p

Hence the tenth term is a10 = 54 - 8p

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