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If the sum of n terms of an AP is 3n^2+2n, find its r^th term.

Asked by Ananya 20th February 2018, 1:12 PM
Answered by Expert
Answer:
begin mathsize 16px style Let space straight t subscript 1 equals straight a equals First space term space and space straight t subscript 2 space end subscript equals second space term space of space the space sequence.
straight S subscript straight n space equals 3 straight n squared plus 2 straight n
straight S subscript 1 space equals space straight a equals 3 cross times 1 plus 2 cross times 1 equals 5
straight S subscript 2 space equals 3 cross times 4 plus 2 cross times 2
straight S subscript 2 equals 16
5 plus straight t subscript 2 equals 16
straight t subscript 2 equals 16 minus 5
straight t subscript 2 equals 11
Hence comma space straight d equals straight t subscript 2 minus straight a
straight d equals 11 minus 5 equals 6
straight a equals 5 comma space straight d equals 6
straight t subscript straight r equals straight a plus open parentheses straight r minus 1 close parentheses straight d
straight t subscript straight r equals 5 plus open parentheses straight r minus 1 close parentheses cross times 6
straight t subscript straight r equals 5 plus 6 straight r minus 6
straight t subscript straight r equals 6 straight r minus 1 end style
Answered by Expert 20th February 2018, 1:50 PM
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