CBSE Class 10 Answered
If the mth term of an ap is 1/n and nth term of an ap is 1/m then find the value of (mn)th
Asked by Yadavrishabh864 | 25 Mar, 2019, 10:11: AM
Let a be the first term and d be the common difference.
mth term of an A.P is
.
![begin mathsize 16px style 1 over straight m end style](https://images.topperlearning.com/topper/tinymce/cache/c3fdb2be7d5e3ebf423462859f57ec36.png)
am = a + (m - 1)d
![begin mathsize 16px style rightwards double arrow straight a space plus space md space minus space straight d space equals space 1 over straight n space space space.... space space left parenthesis straight i right parenthesis
straight n to the power of th space term space of space an space straight A. straight P space is space 1 over straight n.
straight a subscript straight n space equals space straight a space plus space left parenthesis straight n space minus 1 space right parenthesis straight d space
rightwards double arrow space straight a space plus space nd space minus space straight d space equals space 1 over straight m space space space space.... space space left parenthesis ii right parenthesis
Subtract space left parenthesis ii right parenthesis space from space left parenthesis straight i right parenthesis comma space we space get
straight d space equals space 1 over mn
Put space space straight d space equals 1 over mn space in space equation space left parenthesis straight i right parenthesis comma space we space get
straight a space equals 1 over mn
space space
To space find space mn to the power of th term colon
straight a subscript mn space equals space straight a space plus space left parenthesis mn space minus space 1 right parenthesis straight d space equals space 1 over mn plus space left parenthesis mn space space minus space 1 right parenthesis space 1 over mn space equals space 1 end style](https://images.topperlearning.com/topper/tinymce/cache/c70784a21a64515227525f3ed81c2a14.png)
Answered by Yasmeen Khan | 25 Mar, 2019, 11:23: AM
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