Permutations and Combinations

Permutations and Combinations

Question

Which term of the sequence space space 24 comma space 23 1 fourth comma space 22 1 half comma space 21 3 over 4 comma space space..... is the first negative term?

Answer

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#6 {main}</pre> is an A.P. with a = 24, straight d equals 23 1 fourth minus 24 space equals space minus 3 over 4
Let the nth term of the given A.P. be the first negative term.
Then,             straight T subscript straight n space equals space straight a space plus space left parenthesis straight n minus 1 right parenthesis straight d space less than 0.
or            24 + (n - 1) open parentheses negative 3 over 4 close parentheses space less than space 0          or      96 - 3n + 3 < 0
or                         99 - 3n < 0                or                3n > 99
or                                  n > 33
Since 34 is the natural number just greater than 33.

∴  n = 34, Hence, 34th term of the given A.P. is the first negative term.

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