**Arithmetic sequence worksheet solution1 :**

Here we 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) ,……………….

Hence 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 = t_{2}
– t_{1}

= 120 – 125

= -5

General term of an A.P

(t_{n})
= a + (n - 1) d

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

= 125 + 14 (-5)

= 125 – 70

t₁₅ = 55

Hence, 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 = t_{2}
– t_{1}

= 23 ¼ – 24

= (93/4) – 24

= (93-96)/4

d = -3/4

t_{n} = a + (n - 1) d

Let us consider 3 as nth term

t_{n} = 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

Hence, 29^{th} term of
and A.P is 3.

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

**Solution :**

First term (a) = √2

Common difference (d) = 3 √2 - √2 = 2 √2

n = 12

General term of an A.P

t_{n} = a + (n - 1) d

t_{₁}_{₂} = √2 + (12 - 1) (2√2)

= √2 + 11 (2√2)

= √2 + 22 √2

= 23 √2

Hence, 12th of A.P is 23 √2

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

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