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-

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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