Question

Determine the ap whose fifth term is 19 and difference of eight term from thirteen term is 20

Answer 1

Answer:

Fifth term is 19

a+(5-1)d=19

a+4d=19.............(i)

13th term-8th term is 20

a+(13-1)d - (a+(8-1)d) = 20

a+12d-a-7d=20

5d=20

d=4

Putting d=4 in equation (i)

a+4*4=19

a=19-16

a=3

A.P. is a,a+d,a+2d..........

3,3+4,3+2*4.......

3,7,11...........

Answer 2

Answer:

=>3,7,11,15,

Step-by-step explanation:

a5 = a a+ (5-1)d = 19 and [a+(13-1)d] - [a+(8-1)d] = 20 [∵an = a+(n-1)d]

⇒ a + 4d = 19

and a + 12d - a - 7d = 20 ⇒ 5d = 20     

∴  d = 4

On putting d = 4 in Eq.(i), we get 

a + 4(4) = 19

a + 16 = 19 

a = 19 - 16 = 3

So, required AP is a,a+d,a+2d,a+3d,...i.e,,3,3 + 4,3 + 2(4),3 + 3(4),..

i.e.,3,7,11,15,