Arithmetic progressions excercise 5.1

-
Question no 2)
Write first four term of the A.P. when the first term of a and the common difference d are given as follows

A) a = 10 d = 10 
Solutions
Let the series of a1, a2,a3, a4,a5.....
a1= a=10 
a2= a1+d
    = 10+10 = 20
a3 = a2+d
     = 20+10 = 30
a4 = a3+d
     = 30+10 = 40 
a5 = a4+d
     = 40+10 = 50
Therefore the series will be 10,20,30,40,50
First four terms of this A.P. will be 10,20,30,40........

B) a= -2 , d= 0
Let the series be a1, a2, a3,a4.......
a1 = a= -2
a2 = a1+d
     = -2+0 =-2
a3 = a2+d
     = -2+0 = -2
a4 = a3+d
     = -2+0 = -2
Therefore the series will be -2,-2,-2,-2
First four terms of the A.P. will be -2,-2,-2,-2......

C) a=4, d= -3
Let the series be a1, a2, a3,a4.......
a1= a = 4
a2= a1+d
    = 4-3  = 1
a3= a2+d 
    = 1-3 = -2
a4 = a3+d
     = -2-3 =-5
First four terms of the A.P. will be 4,1,-2,-5.....

D) a=-1, d=½

Let the series be a1, a2, a3,a4.......
a1= a= -1
a2= a1+d
   = -1+½=-½
a3= a2+d
    =-½+½= 0
a4=a3+d
    =0+½=½
First four terms of the A.P. will be -1,-½,0,½.......

E) a=-1.25, d=-0.25

Let the series be a1, a2, a3,a4.......
a1 = a=-1.25
a2 = a1+d
     = -1.25-.25 = -1.50
a3 = a2+d 
     =-1.50-0.25 = -1.75
a4 = a3+d 
     = -1.75-0.25 = -2.00
First four terms of the A.P. will be -1.25,-1.50,-1.75,-2.00.......

Comments

Post a Comment

Popular posts from this blog

Grade of concrete

-
Grade of concrete                                   Grade of concrete is defined as the minimum strength the concrete must possess after 28 days of construction with proper quality control. Concrete grade Grade                  Proportion  M 5.                      1: 5 : 10          M7.5.                    1 : 4 : 8        M10                      1 : 3 : 6    M15.                    1 : 2 : 4    M20.                    1 : 1.5 : 3    M25.                  ...
Read more

10 class math airthmatic progessions excerise 5.1

-
Excerise no 5.1 1) In which of the following situations, does the list of number involved makes as airthmatic progessions and why ?   A) the taxi fare after each km when the fare is RS 15 for the first km and RS 8 for each additional km  Answer    It can be observed that  Taxi fare for 1st km = 15   Taxi fare for first 2nd km = 15+8 = 23 taki fare for first 3rd km  = 23+8 = 31 Taki fare for first 4 km    =31+8 = 39 Clearly 15, 23, 31, 39 form an A.P. because every term is 8 more than preceding term. B) the amount of air present in the cylinder when a vaccum pump remove 1/4 À of the air remaining in the cylinder at a time Answer  Let the initial volume of air in a cylinder by V litres . In each stock the vaccum pump remove À 1/4 À of air remaining in the cylinder at a time . In other words after every Stoke only 1- 1/4 = 3/4 Part of air will remain Therefore volume will be V, 3V/4 , (3V...
Read more

Spread Foundation | open Foundation

-
Image
Spread Foundation or open Foundation The Foundation which is constructed over a large area to form a wide base over which the whole structure rests is called spread or open Foundation. These Foundations are made with increasing the base by making off sets. It is a type of shallow Foundation. this type of Foundation is constructed in open excavation by increasing the area at the base of structure by means of offsets or batter. This is most common type of Foundation and is practicable for a depth of about 5 m and is generally convenient above the water table. This Foundation is provided for bridges of moderate height built on sufficiently firm dry ground. If the ground is not stiff the bearing surface is further extended by wide layers of line concrete at the bottom. Method of construction                                             Excavate the Foundation trench to the...
Read more