Question

If a be the first term, d the common difference and l the last term of a given AP then show that is nth term from the end is {1-(n-1)d}

Answer 1

See the photo attached for solution

Answer 2

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$we \: may \: write \: the \: given \: ap \: as \: \\ \implies \: a ,\: (a + d) ,\: (a + 2d).............(l - 2d), \: (l - d) ,\: l \\ thus \: we \: have \: \\ last \: term = l = l - (1 - 1)d \\ 2nd \: last \: term = (l - d) = l - (2 - 1)d \\ 3rd \: last \: term = (l -2d) = l - (2 - 1) \\ \therefore \: nth \: term \: from \: last \: = l - (n - 1)d$