Question

which term of the ap 45, 42 ,39 ,
36 is a first negative term​

Answer 1

Step-by-step explanation:

a=45

d=-3

n=?

l<0

l=a+(n-1)*d

0>45+(n-1)*-3

0-45>(n-1)*-3

(-45/-3)>n-1

15+1>n

16>n will be a positive term

So, n=17 for the first negative term

Answer 2

Given,

AP:  45, 42 ,39 ,36

a = 45

To Find,

First negative term of Ap=?

Solution,

Common difference  = $a_2 - a_1$

Common difference(d) = 42 - 45 = -3

The common difference is negative which means AP is decreasing and will have negative terms too.

From the formula of the nth term in AP, we know that

$a_n = a + (n-1)d$

And the nth term should be negative

$0 > 45+(n-1)*-3$

$0 - 45 > (n-1) * (-3)$

$-45 / -3 > n-1$

$15 + 1 > n$

$n < 16$

Therefore, n should be greater than 16. Let n = 17

$a_{17} = 45 + (17 -1) *-3\\a_{17} = 45 -(3*16)\\a_{17} = 45- 48 \\a_{17} = -3$

Hence, at n = 17, -3 will be the first negative term​ in the AP.