2528, 53, 153, 378, 778, ?
A1485
B1459
C1403
D1489
Answer: C
Explanation:
$\begin{array}{cc}
Pattern & Series \\
28 & 28 \\
28 + 25 × 1^2 & 53 \\
53 + 25 × 2^2 & 153 \\
153 + 25 × 3^2 & 378 \\
378 + 25 × 4^2 & 778 \\
778 + 25 × 5^2 &1403 & \checkmark\\
\end{array}$
122, 213, 340, 509, ?, 997
A726
B859
C849
D729
Answer: A
Explanation:
$\begin{array}{cc}
Pattern & Series \\
5^3-3 & 122 \\
6^3-3 & 213 \\
7^3-3 & 340 \\
8^3-3 & 509 \\
9^3-3 & 726 &\checkmark\\
\end{array}$
112, 119, 133, 154, 182, 217, ?
A269
B289
C249
D259
Answer: D
Explanation:
$\begin{array}{cc}
Pattern & Series \\
112 & 112 \\
112 + 1 × 7 & 119 \\
119 + 2 × 7 & 133 \\
133 + 3 × 7 & 154 \\
154 + 4 × 7 & 182 \\
182 + 5 × 7 & 217 \\
217 + 6 × 7 & 259 &\checkmark\\
\end{array}$
1, 2, 5, 14, 41, 122, ?
A369
B389
C365
D359
Answer: C
Explanation:
$\newcommand\pad[1]{\rlap{#1}\phantom{120}}
\begin{array}
\pad{1} &&\pad{2} &&\pad{5} &&\pad{14} &&\pad{41} &&\pad{122} &&\pad{?}\\
&\pad{3^0} &&\pad{3^1} &&\pad{3^2} &&\pad{3^3} &&\pad{3^4}&&\color{red}{3^5}
&& \Leftarrow\text{1st Diff.} \\
\end{array}$
12, 24, 60, 180, 630, 2520, ?
A11350
B11340
C15482
D15559
Answer: B
Explanation:
$\begin{array}{cc}
Pattern & Series \\
12 & 12 \\
12 × 2 & 24 \\
24 × 2.5 & 60 \\
60 × 3 & 180 \\
180 × 3.5 & 630 \\
630 × 4 & 2520 \\
2520 × 4.5 & 11340 &\checkmark\\
\end{array}$
16, 14, 25, 71, 279, ?
A1389
B1140
C1482
D1559
Answer: A
Explanation:
$\begin{array}{cc}
Pattern & Series \\
16 & 16 \\
16 × 1 - 2 & 14 \\
14 × 2 - 3 & 25 \\
25 × 3 - 4 & 71 \\
71 × 4 - 5 & 279 \\
279 × 5 - 6 & 1389 & \checkmark \\
\end{array}$
6, 46, 126, 286, 606, ?
A1289
B1240
C1282
D1246
Answer: D
Explanation:
$\begin{array}{cc}
Pattern & Series \\
6 & 6 \\
6 + 20 × 2 & 46 \\
46 + 40 × 2 & 126 \\
126 + 80 × 2 & 286 \\
286 + 160 × 2 & 606 \\
606 + 320 × 2 & 1246 &\checkmark\\
\end{array}$
17, 20, 28, 43, 67, ?
A100
B120
C102
D106
Answer: C
Explanation:
$\begin{array}{cc}
Pattern & Series \\
17 & 17 \\
17 + 2^2-1 & 20 \\
20 + 3^2-1 & 28 \\
153 + 4^2-1 & 43 \\
378 + 5^2-1 & 67 \\
778 + 6^2-1 & 102 & \checkmark\\
\end{array}$
