Question

class 10th icse Arithmetic progression

Find the 25th term of the sequence -5, -5/2, 0, 5/2,.....

Answer 1

$Given \: A.P : -5 ,\frac{-5}{2} ,0, \frac{5}{2},\ldots$

$First \:term \: (a = a_{1}) = -5$

$Common \: difference (d) = a_{2} - a_{1}$

$= \frac{-5}{2} - (-5)$

$= \frac{-5}{2} + 5$

$= \frac{-5+10}{2}$

$= \frac{5}{2}$

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

$Here, a = -5, d = \frac{5}{2} \:and \: n = 25$

$25^{th} \:term = a_{25}$

$= a + (25 - 1) d$

$= a + 24d$

$= -5 + 24 \times \frac{5}{2}$

$= -5 + 12 \times 5$

$= -5 + 60$

Therefore.,

$\red{ 25^{th} \:term \: of \: given \:A.P }$

$\green {= 55}$

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