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Question

The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.

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Solution

Given 6th and 17th terms of an AP are 19 and 41 respectively.
Therefore,
a subscript 6 equals a plus left parenthesis 6 minus 1 right parenthesis d equals 19 rightwards double arrow a plus 5 d equals 19 space.... space i right parenthesis A l s o comma a subscript 17 equals a plus left parenthesis 17 minus 1 right parenthesis d equals 41 rightwards double arrow a plus 16 d equals 41 space space... space i i right parenthesis F r o m space i right parenthesis space a n d space i i right parenthesis a plus 16 d minus left parenthesis a plus 5 d right parenthesis equals 41 minus 19 rightwards double arrow 11 d equals 22 rightwards double arrow d equals 2 P u t t i n g space d equals 2 space i n space e q u a t i o n space i right parenthesis rightwards double arrow a plus 5 left parenthesis 2 right parenthesis equals 19 rightwards double arrow a equals 9. N o w comma a subscript 40 equals a plus left parenthesis 40 minus 1 right parenthesis d space space space space space space equals 9 plus 39 cross times 2 space space space space space space equals 87

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