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Between 1 and 31, m no. …

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Between 1 and 31, m no. have been inserted in such a way that the resulting sequence is an A.P and the ratio of 7th and (m-1)th no. is 5:9 . Find the value of m

Posted by Anushka Shekhawat 4 years, 7 months ago

CBSE > Class 11 > Mathematics

1 answers

Sia ? 4 years, 7 months ago

1, A₁, A₂, A₃, ----- A_m, 31 are in AP.
a = 1
a_n = 31

{tex}a _ { m + 2 } = 314{/tex}

a_n = a + (n - 1)d
31 = a + (m + 2 - 1)d

{tex}d = \frac { 30 } { m + 1 }{/tex}

{tex}\frac { A 7 } { A _ { n - 1 } } = \frac { 5 } { 9 }{/tex} (Given)

{tex}\frac { 1 + 7 \left( \frac { 30 } { m + 1 } \right) } { 1 + ( m - 1 ) \left( \frac { 30 } { m + 1 } \right) } = \frac { 5 } { 9 }{/tex}

m = 1

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