If $(x + 1), 3 x$ and $(4 x + 2)$ are the first three terms of an A.P., then the value of $5^{t h}$ term is

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Solution

$(x + 1), 3 x, (4 x + 2)$ are in A.P.
$(x + 1) + (4 x + 2) = 2 \times 3 x \Rightarrow 5 x + 3 = 6 x \Rightarrow x = 3$
Therefore, the A.P. is $4, 9, 14$
$d = 9 - 4 = 5$

Now, $T_{5} = a + (5 - 1) d$
$\Rightarrow T_{5} = 4 + 4 \times 5 ∴ T_{5} = 24$

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