Question

Find the 25th term of the A.P. -5, -5/2, 0, 5/2, ……..

Answer 1

${\bold {\boxed{\underline {\huge {\pink {Answer :}}}}}}$

Given A.P. ->

-5, -5/2, 0, 5/2,...

$now \: for \: the \: {25}^{th} \: term \: = \\ a + 24d - - - (1)$

$where \: a \: is \: the \: first \: term \: and \: \\ d \: is \: the \: common \: diffrence$

$so \: a = - 5 \\ d = a_2 - a_1 \\ = - \frac{5}{2} - ( - 5) \\ - \frac{5}{2} + 5 = \frac{ - 5 + 10}{2} = \frac{ - 5}{2}$

$on \: putting \: in \: equation \: (1)$

$- 5 + 24( \frac{ - 5}{2} ) \\ - 5 - 12 \times 5 \\ - 5 - 60 \\ - 65$

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$so \: the \: 25^{th} term \: is \: \\ - 65$