मराठी

Find the Value of X for Which the Numbers (5x + 2), (4x - 1) and (X + 2) Are in Ap.

Advertisements
Advertisements

प्रश्न

Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.

Advertisements

उत्तर

It is given that (5x + 2),(4x -1) and  (x+2) are in AP.

∴ (4x -1)- (5x +2) = (x+2) - (4x-1)

⇒ 4x -1 - 5x -2 = x+2 -4x +1

⇒ -x -3 = -3x+3

⇒ 3x -x=3+3

⇒2x=6

⇒ x =3

Hence, the value of x is 3.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Arithmetic Progression - Exercises 2

APPEARS IN

आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 5 Arithmetic Progression
Exercises 2 | Q 2

संबंधित प्रश्‍न

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.


200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?


If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?


Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.


Find the sum of all natural numbers between 200 and 400 which are divisible by 7.


Find the first term and common difference for the A.P.

`1/4,3/4,5/4,7/4,...`


In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?


Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.


The common difference of an A.P., the sum of whose n terms is Sn, is


The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is 

 

The term  A.P is 8, 10, 12, 14,...., 126 . find A.P.


Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h1 in the first hour and thereafter increasing the speed by 0.5 km h1 each succeeding hour. After how many hours will the two cars meet?


Q.4


Find the sum of natural numbers between 1 to 140, which are divisible by 4.

Activity: Natural numbers between 1 to 140 divisible by 4 are, 4, 8, 12, 16,......, 136

Here d = 4, therefore this sequence is an A.P.

a = 4, d = 4, tn = 136, Sn = ?

tn = a + (n – 1)d

`square` = 4 + (n – 1) × 4

`square` = (n – 1) × 4

n = `square`

Now,

Sn = `"n"/2["a" + "t"_"n"]`

Sn = 17 × `square`

Sn = `square`

Therefore, the sum of natural numbers between 1 to 140, which are divisible by 4 is `square`.


Find S10 if a = 6 and d = 3.


Find t21, if S41 = 4510 in an A.P.


The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.


An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.


Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :

Activity: 

Given A.P. : 7, 13, 19, 25, ..........

Here first term a = 7; t19 = ?

tn + a + `(square)`d .........(formula)

∴ t19 = 7 + (19 – 1) `square`

∴ t19 = 7 + `square`

∴ t19 = `square`


Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.

Reason (R): The sum of first n odd natural numbers is n2.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×