The second and eight term of an arithmetic progression are 17 and -1 respectively. what is the 14th Term

 Solution

We know that an=a+(n-1)d

and Given that 2nd term of arithmetic progression=17 

 means a2 =17

 then a+d=17 -----------(i)

 and 8th term of arithmetic progression=1 

 means a8 =1

 then a+7d=-1 ----------(ii)

From Equation (i) and (ii) 

a+d=17 -----------(i)

a+7d=-1 ----------(ii)

After solving Equation

a =20

d=-3

now,14 th term  of Ap=

a14 =a+13d

     = 20+13(-3)

    =20-39=-19