Question

Find the first negative number in ap : 14,11,8

Answer 1

Answer:

♧$\large{\boxed{\green{\mathcal{Answer-}}}}$♧

♤AP : 14 , 11 , 8

♡HERE ,

♤A = 14 , D = -3

♡TO FIND :

THE FIRST NEGATIVE TERM IN THE AP.

♤PROOF :

♤ACCORDING TO THE AP.

WE GET ,

14 - 3 = 11

11 - 3 = 8

8 - 3 = 5

5 - 3 = 2

◇2 - 3 = -1 ✔

➡THE FIRST NEGATIVE TERM IN THE AP. IS -1 .

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Answer 2

Question:

Find the first negative number in ap : 14,11,8

Theory :

${\purple{\boxed{\large{\bold{a _{n} = a + (n - 1)d}}}}}$

Solution :

Given Ap series:

14,11,8.....

In this series ;

first term ,a = 14

common difference ,d = 11-14 = -3

_________________________

we have to find first negative term in the given AP series .

⇒ The value of a+(n-1) d < 0

a+(n-1)d < 0

⇒ 14 + (n-1) -3 < 0

⇒14-3n +3 <0

⇒ 17 - 3n <0

⇒3n <17

⇒$n < \frac{17}{3}$

as n is a integer, the first value which satisfies the above condition is n = 6

Now,

$a _{6} = a + (6- 1)d$

⇒ $a _{6} = 14+ (6- 1)-3$

⇒$a _{6} = 14 -18 +3$

⇒$a _{6} = -1$

__________________________

Therefore first negative no is -1