Question

Determine an ap whose 5 term is 19 and difference of eight term from thirteenth term is 20​

Answer 1

Answer:

Let the first term be a and common difference is d. 5th term is (a+4d). Difference between 8th term and 13th term => a+12d -(a+7d) => 5d=20 =>d=4. So 5th term is given 19 So 19=a+4(4)=> a=19-16=3. So the arithematic progression is 3,7,11,15,19,23,27,31,35,39,43,47,51.

Answer 2

Hey there!

Given,

5th term = 19

T₅ = 19

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

and,

13th term - 8th term = 20

T₁₃ - T₈ = 20

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

a + 12d - a - 7d = 20

5d = 20

d = 20 / 5

d = 4

Putting value of d in eq. (i):

a + 4d  = 19

a + 4 * 4 = 19

a = 19 - 16

a = 3

Now,

A.P is given as:

a, a + d , a + 2d , (a+3d) ............

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

3 , 7 , 11, 15........

Hope It Helps You!