1. Tardigrade
  2. Question
  3. Mathematics
  4. Given a sequence a1, a2, a3, ldots ldots . . . . an in which the sum of the first m terms is S m = m 2-5 m then which of the following is not true?

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Q. Given a sequence $a_1, a_2, a_3, \ldots \ldots . . . . a_n$ in which the sum of the first $m$ terms is $S _{ m }= m ^2-5 m$ then which of the following is not true?

Sequences and Series

Solution:

$ S _{ m }= m ^2-5 m $
$S _{ m -1}=( m -1)^2-5( m -1) $
$S _{ m -1}= m ^2+1-2 m -5 m +5 $
$a _{ m }= S _{ m }- S _{ m -1}=2 m -6$
$ \Rightarrow \text { AP also now } a _5=4 ; a _6=6$