Question Detail

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}

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. 20, 19, 17, (...) , 10, 5

Answer: Option D

Explanation:

Pattern in the series is -1, -2, .., .. , -5

So next term will be 17 - 3 = 14

3. In the series 3, 9, 15.. what will be the 21st term ?

Answer: Option A

Explanation:

We can judge that it is A.P.
With 6 as difference
nth term in A.P. = a+(n-1)d
a= 3, n = 21, d = 6
So, 21st term will be = 3+(20)6 = 123

4. 11, 12, 17, 18, 23, 24, (....) . Which term will come next ?

Answer: Option B

Explanation:

Please check, given sequence is combination of two seies
[Note: Usually when terms are more than 5, then chances are there that it may contain 2 series.]

Series 1 = 11, 17, 23
Series 2 = 12, 18, 24

So there is pattern +6 in each term
Next term will be 23+6 = 29

5. 1, 2, 5, 12, 27, 58, 121, ?

Answer: Option A

Explanation:

Pattern in the series is *2+1, *2+2, *2+3,.....

Term which replaces the question mark in the series is
121 * 2 + 6 = 248