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In an A.P if mth term is n and nth term is m,where m =!(not equal to) n,find the pth term.
I substituted for An=a+(n-1)d. (ie Am=a+(m-1)d and An=a+(n-1)d) I don't understand the rest. 
Please explain the steps.

Asked by Deebu 28th November 2014, 6:25 AM
Answered by Expert
Answer:
L e t space apostrophe a apostrophe space b e space t h e space i n i t i a l space t e r m space a n d space apostrophe d apostrophe space b e space t h e space c o m m o n space d i f f e r e n c e space o f space t h e space g i v e n space A P. T h e r e f o r e comma space t subscript n equals a plus open parentheses n minus 1 close parentheses d a n d t subscript m equals a plus open parentheses m minus 1 close parentheses d A l s o space g i v e n space t h a t space t subscript n equals m space a n d space t subscript m equals n rightwards double arrow a plus open parentheses n minus 1 close parentheses d equals m space a n d space a plus open parentheses m minus 1 close parentheses d equals n rightwards double arrow a equals m minus open parentheses n minus 1 close parentheses d space a n d space a equals n minus open parentheses m minus 1 close parentheses d rightwards double arrow m minus open parentheses n minus 1 close parentheses d space equals n minus open parentheses m minus 1 close parentheses d rightwards double arrow m minus n d plus d space equals n minus m d plus d rightwards double arrow m minus n d equals n minus m d rightwards double arrow m d minus n d equals n minus m rightwards double arrow open parentheses m minus n close parentheses d equals n minus m rightwards double arrow d equals fraction numerator open parentheses n minus m close parentheses over denominator open parentheses m minus n close parentheses end fraction rightwards double arrow d equals minus 1 S u b s t i t u t i n g space t h e space v a l u e space o f space d space i n space t h e space e q u a t i o n space a equals m minus open parentheses n minus 1 close parentheses d comma space w e space h a v e comma a equals m minus open parentheses n minus 1 close parentheses open parentheses minus 1 close parentheses rightwards double arrow a equals m plus n minus 1 T h e n space p t h space t e r m space i s space t subscript p equals a plus open parentheses p minus 1 close parentheses d space space space equals m plus n minus 1 plus open parentheses p minus 1 close parentheses open parentheses minus 1 close parentheses space space space equals m plus n minus 1 minus p plus 1 space space space equals m plus n minus p
Answered by Expert 28th November 2014, 9:47 AM
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