The first three terms of an arithmetic series are p, 5p – 8, and 3p + 8 respectively. (a) Show that p=4 (b) Find the value of the 50th term in the series.

(a) If the sequence = p , 5p-8 and 3p+8 is an arithmetic sequence then the difference between successive terms must be constant.e.g. (5p-8)-(p) = (3p+8)-(5p-8)=> 4p-8 = -2p+16 => 6p = 24 => p=24/6 = 4(b) general rule for sequences = a + (n-1)dwhere a = first term ( so in this case a = p = 4 ) and d = common difference ( so in this case d = 5p - 8 -p = 8 )term 50 = 4 + 49(8) = 396