The 5th term of an arithmetic sequence is 38 and the 9th term is 66. What its 10th term is

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Solution

The correct option is C
73

$x_{5} = 28 & x_{9} = 66$

$\Rightarrow x_{1} + 4 d = 38$ & $x_{1} + 8 d = 66$

Solving

$x_{1} + 4 d = 38 x_{1} + 8 d = 66 - - - - ------------- - - 4 d = - 28 d = 7$

$∴ x_{1} + 4 (7) = 38$

$x_{1} = 38 - 28$

$x_{1} = 10$

$∴$ 10th term $= x_{10} = x_{1} + 9 d$

=10+9(7)

=10+63

=73

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