If the sum of the first ten terms of an `A.P` is four times the sum of its first five terms, the ratio of the first term to the common difference is:

Question

If the sum of the first ten terms of an `A.P` is four times the sum of its first five terms, the ratio of the first term to the common difference is:

If the sum of the first ten terms of an `A.P` is four times the sum of its first five terms, the ratio of the first term to the common difference is:
A. `(1)/(2)`
B. 2
C. `(1)/(4)`
D. 4

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

55. Equal and opposite charge is given to two parallel plates. Without any space between them, the electric field is \( 3 \times 10^{5} V / m \) and with space filled with dielectric, electric field intensity is \( 1.0 \times 10^{5} V / m \). The induced charge density on the surface of the dielectric is: (a) \( 3.44 \times 10^{-6} C / m ^{2} \) (b) \( 8.8 \times 10^{-6} C / m ^{2} \) (c) \( 6.93 \times 10^{-6} C / m ^{2} \) (d) \( 1.77 \times 10^{-6} C / m ^{2} \)

2 Answers 5 Views

When the ninth term of an AP is divided by its second term we get 5 as the quotient, when the thirteenth term ia devided ny sixth term the quotient is

2 Answers 4 Views

Consider an AP with a as the first term and d is the common difference such that `S_(n)` denotes the sum to n terms and `a_(n)` denotes the nth term o

2 Answers 5 Views

If the arithmetic progression whose common difference is nonzero the sum of first `3n` terms is equal to the sum of next `n` terms. Then, find the rat

2 Answers 4 Views

If `s_1,s_2,s_3` denote the sum of n terms of 3 arithmetic series whose first terms are unity and their common difference are in H.P., Prove that `n=(

2 Answers 4 Views

in a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equ

2 Answers 4 Views

If 100 times the 100th term of an AP with non-zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

2 Answers 4 Views

Soppose that all the terms of an arithmetic progression (AP) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the f

2 Answers 4 Views

what is the energy \( ( kJ / mol ) \) associated with the de-excitation of an electron from \( n=6 \) to \( n= \) \( He ^{+} \)ion? \( 1.36 \times 10^{6} \) (b) \( 1.36 \times 10^{3} \) (c) \( 1.16 \times 10^{3} \) (d) \( 1.78 \times 10^{3} \)

2 Answers 6 Views

In an A.P the sum of the first n terms bears a constant ratio `lamda` with the sum of the next n terms then `lamda` =

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
According to the question, for AP
`S_(10)=4S_(5)`
`(10)/(2)(2a+9d)=4*(5)/(2)(2a+4d)[" by " S_(n)=(n)/(2)[2a+(n-1)d]]`
`10a+45d=20a+40d`
`implies 10a=5d " " implies (a)/(d)=(1)/(2)`

4 views Answered 2023-02-05 15:29