How to write the next three terms of this harmonic sequence? #-1/3#, #-1/4#, #-1/5#, .....

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Answer 1 · 2018-07-08T18:30:29

The next three terms of harmonic sequence are :

#-1/6,-1/7,-1/8#

Note :
#diamondcolor(red)(1/a,1/b,1/c,..."forms a harmonic sequence , "#

#<=>color(blue)(a,b,c, …"forms an arithmetic sequence"#

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Here,

#-1/3,-1/4,-1/5,..."forms the harmonic sequence."#

#=>-3,-4,-5,..."forms the arithmetic sequence"#

where , first term#=a_1=-3and#

common difference #=d=(-4)-(-3)=-1#

#=>#The next three terms of arithmetic sequence are

#:-6,-7,-8#

#=>#The next three terms of harmonic sequence are

#:-1/6,-1/7,-1/8#