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

- Arithmetic progression worksheet
- Arithmetic series worksheet
- Special series
- Sequence
- Arithmetic progression
- Arithmetic series
- Geometric progression
- Geometric series