Page 67 - Mathematics Class - XI

Case-Study Based Questions
Case-Study Based Questions

A sequence whose terms increases or decreases by a fixed number is called an arithmetic progression (A.P.).
In other words, we can say that a sequence is called an arithmetic progression if the difference of a term and
the previous term is always same i.e. a n + 1 – a = constant for all n.
n
This constant or same difference is called the common difference of an A.P. and is denoted by d.
In an A.P., we usually denote the first term by a, common difference by d and the n term by a or T defined as
th
n
n
T = a = a + (n – 1) d
n
n
Also, l = a + (n – 1) d, where l is the last term of sequence.
n
The sum of n terms, S of this A.P. is given by S 2 a ( n 1) d
n n
2
n
Also, l be the last term, then the sum of n terms of this A.P. is S al
n
2
On the basis of above information, answer the following questions.
1. In n term of an AP is given by a = 2n + 1, then its 10 term is equal to
th
2
th
n
(a) 200 (b) 301 (c) 400 (d) Sequence is not an A.P.
2. 11 term of an A.P. → 11, 18, 25 .............. is equal to
th
(a) 80 (b) 81 (c) 71 (d) 70
3. If the sum of n terms of an A.P. is given by S = 3n + 2n , then the common difference of the A.P. is
th
2
n
(a) 3 (b) 2 (c) 6 (d) 4
4. Let S denotes the sum of the first n terms of an A.P., if S = 3S then S : S is equal to
n
n
2n
3n
n
(a) 4 (b) 6 (c) 8 (d) 10
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.
Q. 1. Assertion (A) : The arithmetic mean (A.M.) between two numbers is 34 and their geometric mean
is 16. The numbers are 4 and 64.
Reason (R) : For two numbers a and b, A.M. = A = ab+ and G.M. = G = ab
2
Q. 2. Assertion (A) : The 20 term of the series 2 × 4 + 4 × 6 + 6 × 8 + ......... + n terms is 1680.
th
Reason (R) : If the sum of three numbers in A.P. is 24 and their product is 440. Then the
numbers are 5, 8, 11, or 11, 8, 5.
Q. 3. Assertion (A) : If the third term of a G.P. is 4, then the product of its first five terms is 4 .
5
Reason (R) : Product of first five terms of a G.P. is given as a a aarar.. 2 .
..
r 2 r
Answers

Case-Study Based Questions: 1. (d) 2. (b) 3. (d) 4. (b)
Assertion-Reason Based Questions: 1. (a) 2. (b) 3. (a)

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