arithmetic sequence worksheet solution1

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

= -5

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

15th term of the A.P = 125 + (15 - 1) (-5)

= 125 + 14 (-5)

= 125 – 70

t₁₅ = 55

Therefore 15th term of A.P is 55

(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

t₁₂ = √2 + (12 - 1) (2√2)

= √2 + 11 (2√2)

= √2 + 22 √2

= 23 √2

Therefore 12th of A.P is 23 √2

arithmetic sequence worksheet solution1 arithmetic sequence worksheet solution1

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