Question

if fourth term of an AP is 64 and its 54th term is -61,then its common difference is=

Answer 1

d= Tm -Tn /m-n=-61-64/54-4=-125/50=-2.5

Answer 2

an = a1 + (n - 1)d

Given that the 4th term is 64:

64 = a1 + (4 - 1)d

64 = a1 + 3d ------------------ [ 1 ]

Given that the 54th term is -61:

-61 = a1 + (54 - 1)d

-61 = a1 + 53d ------------------ [ 2 ]

Putting the 2 equation together:

64 = a1 + 3d ------------------ [ 1 ]

-61 = a1 + 53d ------------------ [ 2 ]

[1 ] - [ 2} ;

64 - (-61) = 3d - 53d

125 = -50d

d = 125 ÷ (-50)

d = -2.5

Answer: d = -2.5