**Mixed Questions on Arithmetic Progression :**

Worksheet given in this section will be much useful for the students who would like to recall the concepts in arithmetic progression.

Question 1 :

For an AP, given that a = 7 and d = 3. Find the 8th term.

Solution:

From the given details we have to find nth term

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

a_{n} = 7 + (8 - 1) (3)

a_{8} = 7 + 7 (3)

a_{8} = 7 + 21

a_{8} = 28

Hence the required term is 28.

(ii) a = -18, n = 10, a_{n} = 0 find the common difference.

**Solution :**

we need the find the common difference

a_{n} = 0

a + (n - 1) d = 0

-18 + (10 - 1) d = 0

-18 + 9 d = 0

9 d = 18

d = 2

(iii) d = -3 n = 18 a_{n} = -5, find the first term.

**Solution :**

a_{n} = -5

a + (n - 1) d = -5

a + (18 - 1) (-3) = - 5

a + 17 (-3) = -5

a - 51 = -5

a = -5 + 51

a = 46

(iv) a = -18.9, d = 2.5 and a_{n} = 3.6. Find the value of n.

**Solution :**

a_{n} = 3.6

a + (n - 1) d = 3.6

-18.9 + (n - 1) (2.5) = 3.6

(n -1) 2.5 = 3.6 + 18.9

(n - 1) 2.5 = 22.5

n - 1 = 22.5/2.5

n - 1 = 9

n = 9 + 1

n = 10

(v) a = 3.5,d = 0 and n = 105. Find the general term.

**Solution :**

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

a_{n} = 3.5 + (105 - 1) 0

a_{n} = 3.5 + 104 (0)

a_{n} = 3.5

After having gone through the stuff given above, we hope that the students have recalled all the concepts in arithmetic progression.

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