Question
Wed December 06, 2017 By: Christine Noelle Fernandes

the sum of the first n terms of an AP is 4n^2 +5n. find the AP

Expert Reply
Rashmi Khot
Wed December 06, 2017
begin mathsize 16px style Sum space of space first space straight n space terms space of space an space straight A. straight P. equals 4 straight n squared plus 5 straight n
rightwards double arrow straight S subscript 1 equals 4 left parenthesis 1 right parenthesis squared plus 5 left parenthesis 1 right parenthesis equals 4 plus 5 equals 9 equals straight a equals straight t subscript 1
straight S subscript 2 equals 4 left parenthesis 2 right parenthesis squared plus 5 left parenthesis 2 right parenthesis equals 16 plus 10 equals 26
rightwards double arrow straight t subscript 1 plus straight t subscript 2 equals 26
rightwards double arrow 9 plus straight t subscript 2 equals 26
rightwards double arrow straight t subscript 2 equals 17
Now comma space straight t subscript 2 minus straight t subscript 1 equals 17 minus 9 equals 8 equals straight d
Thus comma space required space straight A. straight P. equals straight a comma space straight a plus straight d comma space straight a plus 2 straight d comma.......
equals 9 comma space 17 comma space 26 comma space 35 comma.........
end style
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