Question

Determine the AP whose 5th term is 19 and the difference of the 8 the term from the 13th term is 20

Answer 1

This ans help to you

Answer 2

Let the first term of an AP be a and common difference d.
Given, a5 = 19 and a13 – a8 = 20   [given]
∴ 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,...