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Which term of the Arithmetic Progression 3, 10, 17,…. Will be 84 more than its 13th term?

Asked by Topperlearning User 22nd September 2017, 3:37 PM
Answered by Expert
Answer:

begin mathsize 12px style The space given space straight A. straight P. space is space 3 comma space 10 comma space 17 comma.....
Here comma space straight a space equals space 3 space and space straight d space equals space 10 space minus space 3 space equals space 7
straight a subscript straight n space end subscript equals space straight a space plus space open parentheses straight n space minus space 1 close parentheses straight d
straight a subscript 13 space equals space 3 space plus space open parentheses 13 space minus space 1 close parentheses 7
space space space space space space space equals space 3 space plus space 12 space cross times space 7 space
space space space space space space space equals space 87
Let space straight n to the power of th space term space be space 84 space more space than space the space 13 to the power of th space term space of space the space given space straight A. straight P.
straight a subscript straight n space minus space straight a subscript 13 space equals space 84
straight a subscript straight n space minus 87 space equals space 84
straight a subscript straight n space equals space 171
3 space plus space open parentheses straight n space minus space 1 close parentheses 7 space equals space 171
3 space plus space 7 straight n space minus space 7 space equals space 171
7 straight n space minus space 4 space equals space 171
7 straight n space equals space 175
straight n space equals space 25
The space 25 to the power of th space term space of space the space given space straight A. straight P. space will space be space 84 space more space than space its space 13 to the power of th space term. end style

Answered by Expert 22nd September 2017, 5:37 PM
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