Question

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20

NCERT Class X
Mathematics - Exemplar Problems

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

Hi,

Let a and d are first term and common difference of an A . P.

nth term = tn = a + ( n - 1 )d----------( 1 )

i) Given t 5 = 19

a + 4d = 19 -------(2)

ii ) differnce of the eighth term from

the thirteeth term = 20

t 13 - t 8 = 20

a + 12d - ( a + 7d ) = 20

a + 12d - a - 7d = 20

5d = 20

d = 20/ 5

d = 5

Put d = 5 in ( 2 )

a + 4d = 19

a + 4 × 5 = 19

a + 20 = 19

a = 19 - 20

a = - 1

Therefore,
a = -1 , d = 5

Required A .P is

a , a+ d , a + 2d , a + 3d , .....

-1 , 4 , 9 , 14, 19 , ....

I hope this will useful to you.

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Answer 2

a5 is ≈ 19 ⇒ a+4d ≈ 19

a13-a8 ≈ 20 ⇒a+12d-[a+7d]≈20

a+12d-a-7d≈20

12d-7d≈20

5d≈20

d≈20÷5

d≈4

Substitute d≈4 in a+4d≈19

a+4×4≈19

a+16≈19

a≈19-16

a≈3

∴AP ; 3,7,11,15..................