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?

Question

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? (A)  a5=5 (B) a5=4 (C) a 6=6 (D) it is an A.P.

Tardigrade Admin · Accepted Answer

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 ⇒ text AP also now a 5=4 ; a 6=6

Q. Given a sequence $a_{1}, a_{2}, a_{3}, \dots\dots .... a_{n}$ in which the sum of the first $m$ terms is $S_{m} = m^{2} - 5 m$ then which of the following is not true?

$a_{5} = 5$

$a_{5} = 4$

$a_{6} = 6$

it is an A.P.

$S_{m} = m^{2} - 5 m$
$S_{m - 1} = (m - 1)^{2} - 5 (m - 1)$
$S_{m - 1} = m^{2} + 1 - 2 m - 5 m + 5$
$a_{m} = S_{m} - S_{m - 1} = 2 m - 6$
$\Rightarrow AP also now a_{5} = 4; a_{6} = 6$

Q. Given a sequence a1​,a2​,a3​,……....an​ in which the sum of the first m terms is Sm​=m2−5m then which of the following is not true?

a5​=5

a5​=4

a6​=6