How many terms of the sequence 13,11,9 ….. make the sum 45? Explain the answer.

Asked by Topperlearning User | 22nd Sep, 2017, 07:30: AM

Expert Answer:

Let the sum of first n terms be 45. Then,

Sn = 45

begin mathsize 12px style straight S subscript straight n equals straight n over 2 open square brackets 2 straight a space plus space open parentheses straight n minus 1 close parentheses straight d close square brackets
straight n over 2 open square brackets 2 cross times 13 space plus space open parentheses straight n minus 1 close parentheses open parentheses negative 2 close parentheses close square brackets space equals space 45
straight n over 2 open square brackets 26 space minus space 2 open parentheses straight n minus 1 close parentheses close square brackets space equals space 45
13 straight n space minus space straight n open parentheses straight n minus 1 close parentheses equals 45
straight n squared space minus space 14 straight n space plus space 45 space equals space 0
open parentheses straight n minus 9 close parentheses open parentheses straight n minus 5 close parentheses space equals space 0
straight n equals 5 space or space space straight n equals 9
end style

Hence, the sum of first 5 or the first 9 terms is 45.

Answered by  | 22nd Sep, 2017, 09:30: AM

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