Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-10)

Sequences and Series (A.P, G.P, H.P)

Total Questions: 50

21. A man saves Rs. 200 in each of the first three months of his service, In each of the subsequent months, his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs.11,040 after: [Haryana PGT 2019]

Correct Answer: (c) 21months
Solution:

22. In a geometric progression consisting of positive terms, each term equal the sum of the next two terms. Then the common ratio of this progression equal: [Haryana PGT 2019]

Correct Answer: (d) 2 sin 18°
Solution:


23. If arithmetic mean, geometric mean and Harmonic mean between two numbers 'a' and 'b' are A, G, and H respectively, then A, G, H will be: [Haryana TGT 2019]

Correct Answer: (c) In Geometric Series
Solution:

If A, G and H be AM, GM and HM of two given positive real numbers 'a'and 'b', respectively then

24. Third term of sequence aₙ = (-1)ⁿ (n-7) is: [Haryana TGT 2019]

Correct Answer: (c) 4
Solution:

25. For what value of 'K'; K+2, 4K-6, 3K-2 are three consecutive terms of an A.P.? [Haryana TGT 2019]

Correct Answer: (c) 3
Solution:

If K+2, 4K-6, 3K-2 are three consecutive terms of an A.P then
⇒ 4K-6 - (K+2) = 3K-2 - (4K-6)
⇒ 3K-8 = -K+4 ⇒ 4K = 12
⇒ K = 3

26. A man with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service and Rs. 1800 after 10 years of service. What was his starting salary? [Haryana TGT 2019]

Correct Answer: (c) Rs. 1300
Solution:

Let the starting salary of man be Rs. 𝓍. If fixed increment is Rs. 𝓎 then
salary after 4 years    𝓍 +4𝓎 = 1500
salary after 10 years    𝓍 + 10𝓎 = 1800
which gives
𝓎 = 50 and hence 𝓍 = 1300
Hence starting salary of the man was Rs. 1300.

27. A square is drawn by joining the mid-points of the sides of a given square. In the same way, this process continues indefinitely. If side of the first square is 4 cm, than the sum of the area of all the squares are equal to: [Haryana TGT 2019]

Correct Answer: (a) 32 cm²
Solution:

28. Let us say a, b, c are in AP then which of the following in not true? [DSSSB TGT 04-09-2021 Shift-I (Male)]

Correct Answer: (c) b+a = c+b
Solution:

29. Find out the common ratio of the GP if the first term of a GP is 1 and the sum of the third term and fifth term is 90 [DSSSB TGT 04-09-2021 Shift-I (Male)]

Correct Answer: (a) 3
Solution:

30. If 5th term and 7th term of a harmonic progression are respectively 7 and 5, then its 35th term will be: [Haryana PGT 2020]

Correct Answer: (b) 1
Solution: