MIXED QUESTIONS ON ARITHMETIC PROGRESSION

Question :

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)

a₈  =  7 + 7 (3)

a₈  =  7 + 21

a₈  =  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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.