CAT 2025 Lesson : Class Discussion: Modern Maths - Progressions: 9 to 16

Question 9

How many integral Arithmetic Progressions with at least 3 elements exist such that the first and last terms are 17 and 101 respectively?

Answer: 11

Question 10

Consider the set of numbers {1, 3,

3^2, 3^3,.....,3^{100}

}. The ratio of the last number and the sum of the remaining numbers is closest to:
[XAT 2016]

		1
		2
		3
		50
		99

Question 11

The 288^th term of the series

a, b, b, c, c, c, d, d, d, d, e, e, e, e, e, f, f, f, f, f, f ...

is
[CAT 2003 First Paper]

		$u$
		$v$
		$w$
		$x$

Question 12

\dfrac{1}{2} + \dfrac{3}{4} + \dfrac{5}{8} + \dfrac{7}{16}+ …

=?

Answer: 3

Question 13

\dfrac{1}{7} + \dfrac{5}{7^2} + \dfrac{14}{7^3} + \dfrac{30}{7^4}+ \dfrac{55}{7^5} …

		$\dfrac{41}{108}$
		$\dfrac{49}{162}$
		$\dfrac{107}{324}$
		$\dfrac{247}{648}$
		99

Question 14

1 + (1 + 5) + (1 + 5 + 9) + …. + (1 + 5 + 9 + … + 77) = ?

Answer: 5530

Question 15

(1 \times 200) + (2 \times 199) + (3 \times 198) + … + (100 \times 101)

=?

Answer: 676700

Question 16

\dfrac{1}{3 \times 8} + \dfrac{1}{8 \times 13} + \dfrac{1}{13 \times 18} + … + \dfrac{1}{98 \times 103}

= ?

		$\dfrac{7}{103}$
		$\dfrac{35}{103}$
		$\dfrac{20}{309}$
		$\dfrac{100}{309}$

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