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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