Permutations and Combinations

Permutations and Combinations

Question

Which term of an A.P. 5, 2, -1, ......... is -22?

Answer

The given A.P. is: 5, 2, - 1,...............
Here a = 5, d = 2 - 5 = -3
Let -22 be the nth term

∴                         straight t subscript straight n space equals space minus 22                or             a + (n - 1)d = -22
or             5 + (n - 1) (-3) = -22             or               5 - 3n + 3 = -22
or                    8 - 3n = -22                   or                       3n = 8 + 22
or                         3n = 30                    or                           n = 10

∴                  -22 is the 10th term.

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