Question

Find the 20th term of an AP whose 3rd term is 7 and the seventh term exceeds three times the 3rd term by 2. Also find its
nth term “​

Answer 1

a3= a+2d

a7= 3(a+2d) + 2 ---------------------------(i)

therefore, a+6d=3a+6d + 2

a=3a+2

a-3a=2

-2a=2

a=-1          -------------------(ii)

to find d, we use equation (i)

so, we get d=4

so, a20= a+19d = -1+ 19(4) = 75

to find an, we substitiue all the values that we found:\

an= -1+ (n-l)4 = -1+4n-4 = 4n-5