Question

in an Ap The 3rd and 7th term are 14 and -2 Respectivly . what term of the ap is 14

Answer 1

Step-by-step explanation:

given

3rd term = 14

or, a+2d=14

or, a=14 - 2d ----equation 1

7th term = -2

or, a+6d = -2

or, (14- 2d)+6d = -2 -------[From equation 1]

or, 14- 2d+6d = -2

or, 14+4d = -2

or, 4d= -2-14

or, d= -16/4

or d= -8

Also,

From equation 1

a =14- 2d

or, a = 14 -2(-8)

or, a= 14+ 16

or, a= 30

At last

a+(n-1)d= 14

or, 30 + (n-1) (-8) = 14

or, (n-1)(-8) = 14-30

or, n- 1 = -16/(-8)

or, n- 1 = 2

or, n= 2+1

or, n= 3

hence,

the 3rd term =14

(the process is to be done by this but the 3rd term is equal to 14 is already given in the question)