Permutations and Combinations

Permutations and Combinations

Question

The sum of first 4 terms of an A.P. is 56. The sum of last 4 terms is 112. If its first term is 11, then find the number of terms.

Answer

Let a be first term, d be common difference, l be the last term of A.P.
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rightwards double arrow space 4 over 2 left square bracket 2 space left parenthesis 11 right parenthesis space plus space left parenthesis 4 minus 1 right parenthesis straight d right square bracket space equals space 56                                     open curly brackets because space space straight S subscript straight n space equals space straight n over 2 left square bracket 2 straight a space plus space left parenthesis straight n space minus space 1 right parenthesis straight d right square bracket close curly brackets
rightwards double arrow            22 + 3d = 28 rightwards double arrow 3d = 6 rightwards double arrowd = 2.
Also, Sum of last 4 terms = 112
rightwards double arrowl + (l -d) + (l - 2d) + (l - 3d) = 112
rightwards double arrow                   41 - 6d = 112    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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Let 31 be the nth term.

∴                               l space equals space straight t subscript straight n space equals space 31 space space rightwards double arrow space space space straight a space plus space left parenthesis straight n space minus space 1 right parenthesis. space straight d space equals space 31
or               11 + (n - 1) 2 = 31           or    (n - 1)2 = 20         or   n - 1 = 10     or    n = 11.

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