Question

Which term of the progression 20,77/4,37/2,54/4... is the first negative term

Answer 1

here,

a = 20 and d= -3/4.

let the first negative term be x th term

therefore,

ax = a + (x-1)d

hence,

a + (x-1)d < 0

20 + (x-1)(-3/4) <0

20 -3x/4 + 3/4 <0

83 / 4 < 3x/4 .......(adding both sides 3x/4)

83 < 3x

x > 83/3

x > 27.66

therefore,

the first negative term will be the 28th term.

hence,

a28 = a + (27)d = 20 + (-81/4) = -1/4