Home
Class 10
MATHS
Which of the following form of an AP ? J...

Which of the following form of an AP ? Justify Your answer.
(i) `-1,-1,-1,-1, …`
(ii) `0, 2, 0, 2, …`
(iii) `1, 1, 2, 2, 3, 3, … `
(iv) `11, 22, 33, … `
(v) `2, 2^(2), 2^(3), 2^(4)`

Text Solution

Verified by Experts

(i) Here, `t_(1)=1, t_(2)= -1, t_(3)= -1` and `t_(4)= -1`
`t_(2)-t_(1)= -1+1=0`
`t_(3)-t_(2)= -1+1=0`
`t_(4)-t_(3)= -1+1=0`
Clearly, the difference of successive terms is same, therefore given list of numbers form an AP.
(ii) Here, `t_(1)=0, t_(2)= 2, t_(3)= 0` and `t_(4)= 2`
`t_(2)-t_(1)= 2-0=2`
`t_(3)-t_(2)= 0-2= -2`
`t_(4)-t_(3)= 2-0=2`
Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP.
(iii) Here, `t_(1)=1, t_(2)= 1, t_(3)= 2` and `t_(4)= 2`
`t_(2)-t_(1)= 1-1=0`
`t_(3)-t_(2)= 2-1=1`
`t_(4)-t_(3)= 2-2=0`
Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP.
(iv) Here, `t_(1)=11, t_(2)= 22` and `t_(3)= 33`
`t_(2)-t_(1)= 22-11=11`
`t_(3)-t_(2)= 33-22=11`
`t_(4)-t_(3)= 33-22=11`
Clearly, the difference of successive terms is same, therefore given list of numbers form an AP.
(v) Here, `t_(1)=(1)/(2), t_(2)= (1)/(3)` and `t_(3)= (1)/(4)`
`t_(2)-t_(1)= (1)/(3)-(1)/(2)=(2-3)/(6)=(1)/(6)`
`t_(3)-t_(2)=(1)/(4)-(1)/(3)=(3-4)/(12)=(1)/(12)`
Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP.
(vi) `2, 2^(2), 2^(3), 2^(4), ...` i.e.,`2, 4, 8, 16, ...`
Here, `t_(1)=2, t_(2)= 4, t_(3)= 8` and `t_(4)= 16`
`t_(2)-t_(1)= 4-2=2`
`t_(3)-t_(2)= 8-4= 4`
`t_(4)-t_(3)= 16-8=8`
Clearly, the difference of successive terms is not same, therefore given list of numbers does not form an AP.
(vii) `sqrt(3),sqrt(12),sqrt(27),sqrt(48), ...` i.e., `sqrt(3),2sqrt(3),3sqrt(3),4sqrt(3), ...`
Here, `t_(1)=sqrt(3), t_(2)= 2sqrt(3), t_(3)= 3sqrt(3)` and `t_(4)= 4sqrt(3)`
`t_(2)-t_(1)= 2sqrt(3)-sqrt(3)=sqrt(3)`
`t_(3)-t_(2)= 3sqrt(3)-2sqrt(3)=sqrt(3)`
`t_(4)-t_(3)= 4sqrt(3)-3sqrt(3)=sqrt(3)`
Clearly, the difference of successive terms is same, therefore given list of numbers form an AP.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    NCERT EXEMPLAR ENGLISH|Exercise Short Answer Type Questions|35 Videos

  • ARITHMETIC PROGRESSIONS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|10 Videos

  • ARITHMETIC PROGRESSIONS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|10 Videos

  • AREAS RELATED TO CIRCLE

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|20 Videos

  • CIRCLES

    NCERT EXEMPLAR ENGLISH|Exercise EXERCISE 9.4 LONG ANSWER TYPE QUESTIONS|14 Videos

Similar Questions

Explore conceptually related problems

Which of the following list of numbers does form an AP? If they form an AP. write the next two terms :(i) 4, 10, 16. 22, . . .(ii) 1,-1, -3,-5, . . .(iii) -2,2,-2,2, . . .(iv)1,1,1,2,2,2,3,3,3, . . .

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0) (ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) (iii) (4, 5), (7, 6), (4, 3), (1, 2)

In which octant the following points lie : (i) (2, 1, 4) (ii) (-1,2,4) (iii) (1,-3, 2) (iv) (1, 5,-6) (v) (2, -1, -3) (vi) (-2, 3, -5) (vii) (-4, -1, 3) (viii) (-1, -2, 3)

Find the distance between the following pairs of points:(i) (2, 3,5) and (4,3,1) (ii) (3,7, 2) and (2,4, 1) (iii) (1, 3, 4) and (1, 3,4) (iv) (2, 1, 3) and (2,1,3) .

Find the distance between the following pairs of points : (i) (-2, 1, -3) and (4, 3, -6) (ii) (9, -12, -8) and (0,0,0) (iii) (2,1,-3) and (2, 3, -3) (iv) (1,0,0) and (4, 4, 5)

By plotting the following points check whether they are collinear or not (i) (1,1), (2,2),(4,4) (ii) (1,0), (-3,0), (0,0) (iii) (2,-2), (0,0), (-3,4)

Compute the adjoint of each of the following matrices: [[1, 2, 2],[ 2 ,1 ,2],[ 2, 2, 1]] (ii) [[1, 2, 5],[ 2, 3,1],[-1, 1, 1]] (iii) [[2,-1, 3],[ 4, 2, 5],[ 0, 4,-1]] (iv) [[2, 0,-1],[ 5, 1, 0],[ 1, 1, 3]] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

Are the following pair of linear equations consistent ? Justify your answer. (i) -3x - 4y = 12 and 4y + 3x = 12 (ii) (3)/(5)x - y = (1)/(2) and (1)/(5) x - 3y = (1)/(6) (iii) 2ax + by = a and 4ax + 2by - 2a = 0, a, b != 0 (iv) x + 3y = 11 and 2(2x + 6y) = 22

Check which of the following are solutions of the equations x-2y=4 and which are not: (i) (0,2) (ii) (2,0) (iii) (4,0) (iv) (sqrt(2),4sqrt(2)) (v) (1,\ 1)

Locate the following points (i) (1,-1,3) " " (ii) (-1,2,4) (iii) (-2,-4,-7) " " (iv) (-4,2,-5)

Home
Profile