Question Detail

19, 2, 38, 3, 114, 4, ? . Which term should replace the question mark in this series ?

Answer: Option C

Explanation:

Please check the given sequence is combination of two series.
Series 1: 19, 38, 114, ...
Series 2: 2,3,4

In series 1, Pattern followed is *2, *3, so next will be *4
Next term will be
114*4 = 456

1. Which fraction will come next, \begin{aligned} \frac{1}{2}, \frac{3}{4}, \frac{5}{8}, \frac{7}{16}, ? \end{aligned}

\begin{aligned} \frac{11}{32} \end{aligned}
\begin{aligned} \frac{9}{28} \end{aligned}
\begin{aligned} \frac{9}{30} \end{aligned}
\begin{aligned} \frac{9}{32} \end{aligned}

Answer: Option D

Explanation:

Numerators of the fractions in the given sequence are getting increased by 2, i.e. 1+2,3+2,5+2, so next will be 7+2 = 9

Denominators of the fractions in the series is getting doubled, 2*2 = 4, 4*2 = 8, 8*2 = 16, no next will be 16*2 = 32

So resulting fraction will be
\begin{aligned}
\frac{9}{32}
\end{aligned}

2. 6, 11, 21, 36, 56, ... ?

Answer: Option A

Explanation:

Pattern is +5, +10, +15, + 20. So next will be 56+25 = 81

3. 1,2,6,24, ?

Answer: Option C

Explanation:

Pattern is *2, *3, *4
So next number is the series will be *5
24*5 = 120

4. In the series 2, 6, 18, 54, ... what will be the 8th term ?

4174
4150
4274
4374

Answer: Option D

Explanation:

We can see the given series is in G.P.
as 2*3 = 6, 6*3 = 18, 18*3 = 54
So a = 2 , r = 3
nth term in G.P. is
\begin{aligned}
ar^{n-1} \\
= 2*3{8-1} \\
= 2*3^7 \\
= 2*2187 = 4374
\end{aligned}