Permutations and Combinations

Permutations and Combinations

Question

Determine the number of terms in an A.P. 3, 8, 13, .......253. Also, find 12th term from the end.

Answer

The given A.P. is : 3, 8, 13, ....., 253
Here, a = 3, d = 8 - 3 = 5
Let there be n terms of an A.P.

∴                   straight t subscript straight n space equals space 253                 or                            l italic space italic equals italic space italic 253
or            a + (n - 1)d = 253            or                 3 + (n - 1) 5 = 253
or             3 + 5n - 5 = 253              or                       5n - 2 = 253
or                  5n = 255                   or                             n = 51
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#6 {main}</pre>

∴    12th term from end = 253 - (12 - 1)5 = 253 - (11) (5) = 253 - 55 = 198

 

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