Question

Which term of the progression 20, 19 4 1 , 18 2 1 , 17 4 3 , ... is the first negative term ?

Answer 1

HI !

20 , 19 1/4 , 18 1/2 , 17 3/4 ......

first term = a = 20 

common difference = d = 19 1/4 - 20 = 77/4 - 20 = -3/4

First negative term would be the term after the term that is zero .

Let us find which term of the A.P is zero .

If the x th term be the zero , then (x + 1)th term is the first negative term 

an = 0

an = a + (n - 1) d

0 = 20 + ( n - 1) -3/4

-20 = (n - 1) -3/4

-20 = -3/4n + 3/4

3/4n = 3/4 + 20

3/4 n = 83/4

n = 83*4/4*3

n = 83/3

n = 27th term ( approx.)

27th term is the term which is zero.

Hence, 28th term is the first negative term 

Answer 2

Which term of the progression 20, 19 4 1 , 18 2 1 , 17 4 3 , ... is the first negative term ?

Solution :19 1/4 =77/4 Now,20-77/4 =3/4

18 1/2 =37/2 Now,77/4-37/2 =3/4

17 3/4 =71/4 Now,37/2-71/4 =3/4

So,we have an arrangement where terms get diminished by 3/4 .Means it is A.P.series with a=20 and d=(- 3/4).Let nth term be its first negative term.

=> 20 +(n-1)(- 3/4) <0

{ in A.P.,nth term =a+(n-1)d

=> 80-3n+3 <0 => 83<3n =>83/3 <n

Along these lines, n =28

{first whole number more prominent than 83/3 ~27.6 }.

Also, 28th term =20+(28-1)(- 3/4)

=20+27×(- 3/4) = - 1/4 Ans