The 7th term of an A.P. is 3p + 5q and the 18th term is 19(2q − p). Find the first three terms of the sequence.


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Question Number 124093 by Don08q last updated on 30/Nov/20

$The 7 t h term of an A . P . is 3 p + 5 q$ $and the 18 t h term is 19 (2 q - p) . Find$ $the first t h r e e terms of the sequence .$
	Answered by liberty last updated on 30/Nov/20

	$T_{7} = 3 p + 5 q; T_{18} = 38 q - 19 p$ $d = \frac{T_{18} - T_{7}}{18 - 7} = \frac{38 q - 19 p - 3 p - 5 q}{11} = \frac{33 q - 22 p}{11} = 3 q - 2 p$ $T_{1} = T_{7} + (1 - 7) d = 3 p + 5 q - 6 (3 q - 2 p)$ $T_{1} = 3 p + 5 q + 12 p - 18 q = 15 p - 13 q$ $T h e f i r s t t h r e e t e r m s o f t h e s e q u e n c e$ $T_{1} = 15 p - 13 q$ $T_{2} = 15 p - 13 q + 3 q - 2 p = 13 p - 10 q$ $T_{3} = 13 p - 10 q + 3 q - 2 p = 11 p - 7 q$
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