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If the 10th term of a harmonic progression is 21 and the 21st term of the same harmonic progression is -10, then find the 210th term.

 Jul 22, 2021
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1/21 =1 / [F + 9D],   

1/-10=1 /[F + 20D], solve for F, 

 

Use substitution to get:

F ==510 / 11  - this is the 1st term

D== - 31 / 11  - this is the common difference

 

210th term   ==[510 /11]  + [- 31/11 * 209]

                     ==[510 /11]  + [- 6479 / 11]

                     == - 5969 / 11  -  this is the 210th term

 Jul 22, 2021

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