Algebra (Mathematics Chapterwise Solved Papers for Teaching) (Part-11)

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

Total Questions: 25

1. The value of 1²+3²+5²+...+ (2n-1)² is [UP PGT-2016 (02-02-2019)]

Correct Answer: (a)
Solution:


2. The least value of 'n', for which 1+3+3²+ ...+ 3ⁿ⁻¹ > 700 is equal to [UP PGT-2016 (02-02-2019)]

Correct Answer: (d) 7
Solution:

3. Solve the following equation? [UP PGT-2016 (02-02-2019)]

Correct Answer: (c)
Solution:

4. Solve the following equation? [UP PGT-2016 (02-02-2019)]

Correct Answer: (a)
Solution:

5. If m is an Arithmetic series and the first term of each of them has unit and common difference 1,2,3....... m respectively. Then what will be the sum of their nI terms? [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (c)
Solution:

Given that m is A.P.
Series for first condition is
Iˢᵗ 2, 3, 4 .......n
(with common different one.)
Formula-
then
IIⁿᵈ series
⇒ 1,3, 5, 7........n (with common difference 2.)
IIIʳᵈ series
⇒ 1, 4, 7, 10 ......n (with common difference 3.)
mᵗʰ series
⇒ 1, m+1, 2m+1,.......n common difference m
Sum of equation (i), (ii), (iii) and (iv)
On solving the sum of n terms

6. Four arithmetic series, The sum of the terms is S₁, S₂, S₃ and S₄ and the first term of each is 2 and common difference is 1,3,5, and 7 respectively then: [DSSSB 23 SEP 2018 (9 AM-11 AM)]

Correct Answer: (d) S₄+S₁ = S₂+S₃
Solution:

7. The sum of three numbers in arithmetic progression is 51 and the product of first and third terms is 273. The common difference in this progression is [LT 2018]

Correct Answer: (b) 4
Solution:

8. The harmonic mean of two numbers is 4. If their arithmetic mean A and geometric mean G satisfy the equation 2A+G²=27, then the numbers are [LT 2018]

Correct Answer: (c) 3,6
Solution:

9. Solve the following equation? [LT 2018]

Correct Answer: (b)
Solution:


10. If x is the first term of a geometric progression and the sum of its infinite terms is 1/3, then x lies in the interval [LT 2018]

Correct Answer: (d)
Solution: