Question

determine the AP whose fifth term is 19 and difference of the 8 term from the 13th term is 20​

Answer 1

Answer:

The A.P is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75........

Step-by-step explanation:

Let 'a' be the first term and 'd' be the common difference.

By formula, Nth term = a + (n-1)d

5th term = a + (5-1)d

thus, 19 = a + 4d                           (equation 1)

8th term = a + 7d

13th term = a + 12d

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

a + 12d - a - 7d = 20

5d = 20

thus d = 4

so, a = 19 - 4d                  (from equation 1)

        = 19 - 16 = 3

so, first term is 3 and 4 gets added on every step

thus we get, 3, 7, 11..................

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Answer 2

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 , ....