Question

which term of A.p 15 ,13¾,12½,11½.......... . . .......
is the first negative term

Answer 1

a₁ = 15
a₂ = 13³/₄ = 55/4
a₃ = 12¹/₂ = 25/2
a₄ = 11¹/₂ = 23/2
d  = a₂ - a₁
    = 55/4 - 15
    = 55-60/4
    = -5/4
0 > 15 + (n-1)-5/4
0 > 15 + 5/4 -5n/4
65/4 > -5n/4
65 > 5n
13 > n
therefore the 12th term of ap is the first negative term. 

Answer 2

Answer: 14th term

Explanation:

a=15, d=13¾-15

= -5/4

Let nth term be first -ve term

Tn= a + (n-1)d

= 15 + (n-1) (-5/4)

= 15 + [ (-5/4n) - (-5/4) ]

= 15 -5/4n + 5/4

= 15 + 5/4 -5/4n

= 65/4 - 5/4n. [ 15×4/4 + 5/4 =

60+5/4 = 65/4 ]

65/4 - 5/4n < 0

-5/4n < -65/4

5/4n > 65/4

n > 65/4 × 4/5

n > 65/5

n > 13

Therefore, 14th term is the first -ve term of the give A.P.

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