Question

What is the 11th term of the sequence: m-2n, m-n, m ,...?

Answer 1

Step-by-step explanation:

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Answer 2

$Given \: sequence\: m-2n, m-n, m ,\cdot\cdot\cdot$

$First \:term (a) = m - 2n$

$a_{2} - a_{1}\\ = m - n - ( m - 2n ) \\= m - n - m + 2n \\= n$

$a_{3} - a_{2}\\= m - ( m - n ) \\= m - m + n \\= n$

$a_{2} - a_{1} = a_{3} - a_{2} = n$

$\therefore The \: sequence \:is \: in \:A.P$

$Common \: differnce (d) = n$

$\boxed{ \pink { n^{th} \: term (a_{n}) = a + (n-1)d }}$

$Here, a = m - 2n, d = n \: and \: n = 11$

$\red{ 11^{th} \:term } \\= a_{11} \\= (m-2n) + ( 11 - 1 )n \\= m - 2n + 10n \\= m - 8n$

Therefore.

$\red{ Required \: 11^{th} \:term } \green {= m - 8n}$

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