CAT 2025 Lesson : Class Discussion: Modern Maths - Progressions: 1 to 8

Class Discussion - Progression

Question 1

1^2 - 2^2 + 3^2 - 4^2 + … + 101^2

=?

Answer: 5151

Question 2

The average of the 5 terms in an increasing Arithmetic Progression is 7. What is the last term of this progression if the sum of their squares is 335?

Answer: 13

Question 3

An Arithmetic Progression has 13 terms. If the average of the first 4 terms is 19 and the average of the last 6 terms is 83, then what is the average of the 13 terms?

Answer: 55

Question 4

The sum of 4 terms in an Arithmetic Progression is 12. The product of the 2nd and 3rd terms is 32 more than the product of the 1st and 4th terms. What is the sum of all possible values that the 4th term can take?

Answer: 6

Question 5

The 3^rd and 8^th terms of an Arithmetic Progression are 64 and 49 respectively. You are required to limit the terms in the sequence such that the sum of the terms is a positive integer. What is the maximum number of terms that you can have in this sequence?

Answer: 47

Question 6

The sum of the first 15 terms of an Arithmetic Progression (AP) is 50 while the sum of the first 45 terms of the AP is 315. What is 10 times the 32^nd term?

Answer: 92

Question 7

If three positive real numbers

a, b

and

c (c > a)

are in Harmonic Progression, then log

(a + c)

+ log

(a - 2b + c)

is equal to:
[IIFT 2008]

		2 log $(c - b)$
		2 log $(a - c)$
		2 log $(c - a)$
		log $a$ + log $b$ + log $c$

Question 8

Suppose

a, b

and

c

are in Arithmetic Progression and

a^2, b^2

and

c^2

are in Geometric Progression. If

a < b < c

and

a + b + c

\dfrac{3}{2}

, then the value of

a

=
[IIFT 2008]

		$\dfrac{1}{2\sqrt{2}}$
		$\dfrac{1}{2\sqrt{3}}$
		$\dfrac{1}{2} - \dfrac{1}{\sqrt{3}}$
		$\dfrac{1}{2} - \dfrac{1}{\sqrt{2}}$

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