# 10th CBSE math solution for exercise 5.2 part 4

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## 10th CBSE math solution for exercise 5.2 part 4

(4) Which term of the AP 3,8,13,18,............ is 78?

Solution:

a = 3     d = t₂ -t₁       a n = 78

= 8 - 3

= 5

a + (n - 1) d = 78

3 + (n - 1) 5 = 78

(n - 1) 5 = 78 - 3

(n - 1) 5 = 75

n - 1 = 75/5

n - 1 = 15

n = 15 + 1

n = 16

Therefore 78 is 16th term of the given sequence

(5) Find the number if terms in each of the following APs:

(i) 7, 13,19,.................205

Solution:

a = 7    d = t₂ -t₁       a n = 205

= 13 - 7

= 6

a n = 205

a + (n -1) d = 205

7 + (n - 1) 6 = 205

(n - 1) 6 = 205 - 7

(n - 1) 6 = 198

n - 1 = 198/6

n - 1 = 33

n = 33 + 1

n = 34

Therefore total number of terms is 34

(ii) 18, 15 ½ , 13,...............,-47

Solution:

a = 18    d = t₂ -t₁       a n = -47

= 15 ½ - 18

= (31/2)  - 18

= (31 - 36)/2

= -5/2

a n = -47

a + (n -1) d = -47

18 + (n - 1) (-5/2) = -47

(n - 1) (-5/2) = -47 - 18

(n - 1) (-5/2) = -65

n - 1 = (-65 x 2)/(-5)

n - 1 = 26

n = 26 + 1

n = 27

Therefore total number of terms is 27.

(6) Check whether -150 is a term of the AP 11,8,5,2,..........

Solution:

a = 11    d = t₂ -t₁       a n = -150

=  8 - 11

= -3

a n = -150

a + (n -1) d = -150

11 + (n - 1) (-3) = -150

(n - 1) (-3) = -150 - 11

(n - 1) (-3) = -161

n - 1 = (-161)/(-3)

n - 1 = 53.6

n = 53.6 + 1

n = 54.6

So -150 is not one of term of the above sequence.