Arithmetic Sequence Worksheet Solution1





In the page arithmetic sequence worksheet solution1 you are going to see solution of each questions from the arithmetic sequence worksheet.

(1) The first term of an A.P is 6 and the common difference is 5. Find the A.P and its general term

Solution:

First term = 6

Common difference = 5

                a = 6

                d = 5

General form of A.P is a , a + d , a + 2 d , …………….

                                 6 , (6 + 5) , (6 + 2(5)) , …………..

                                 6 , 11 , (6 + 10) ,……………….       

Therefore the required arithmetic progression is  6 , 11 , 16 , …………..


(2) Find the common difference and 15 th term of an A.P 125 , 120 ,115 , 110 , ……….…. 

Solution:

First term = 125

               a = 125

Common difference = t2 – t1

                                     = 120 – 125

                                    = -25

General term of an A.P (tn) =  a + (n - 1) d

                                      = 125 + (15 - 1) (-25)

                                      = 125 + 14 (-25)

                                       = 125 – 350

                             t₅   = -225

Therefore 15th term of A.P is -225


(3) Which term of the arithmetic sequence is 24  , 23 ¼ ,22 ½ , 21 ¾ , ………. Is 3?

Solution:

First term = 24

 a = 24

Common difference = t2 – t1

                                     = 23 ¼ – 24

                                     = (93/4) – 24

                                     = (93-96)/4

                                d  = -3/4

 tn =  a + (n - 1) d

Let us consider 3 as nth term

 tn = 3

3 = 24 + (n-1) (-3/4)

3 – 24 = (n-1)  (-3/4)

 (-21 x 4)/(-3) = n -1

 84/3 = n -1

 28 = n – 1

 28 + 1 = n

   n =29

Therefore 29th term of and A.P is 3.  


(4) Find the 12th term of the A.P √2 , 3 √2 , 5 √2 , …………

Solution:

First term = √2

               a = √2

Common difference = 3 √2 - √2  

                                  d = 2 √2

n = 12

General term of an A.P

tn =  a + (n - 1) d

t₂ =  √2 + (12 - 1) (2√2)

     = √2 + 11 (2√2)

     = √2 + 22 √2

     = 23 √2

Therefore 12th of A.P is 23 √2

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