If $10^{t h}$ term of an A.P is $15$ and $15^{t h}$ term is $10$ , then $4^{t h}$ term is

24

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23

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22

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21

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Solution

The correct option is D $21$
Using the formula for nth term of an A.P,
$a_{n} = a_{1} + (n - 1) d$
$a_{10} = a_{1} + 9 d$
Since $a_{10} = 15$

$15 = a_{1} + 9 d$ ...(i)
Similarly
$a_{15} = a_{1} + 14 d$
Since $a_{15} = 10$ , hence
$10 = a_{1} + 14 d$ ...(ii)
Subtracting i from ii
$5 d = - 5$
$d = - 1$
Hence
$a_{1} = 24$
Therefore
$a_{4} = a_{1} + 3 d$
$= 24 - 3$
$= 21$ .

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