Question

which term of an AP is negative for the AP 19,16,13………​

Answer 1

Answer:

as here a=19

d= -3

then an th term will be

-2 = a+(n-1)d

-2=19+(n-1)-3

-19-2=(n-1)-3

-21=(n-1)-3

7=n-1

n=8

so 8th term of ap will be negative

Answer 2

Given: An arithmetic progression.

To find: The term in the AP that is negative.

Answer:

AP - 19, 16, 13, ...

From the given progression, we have:

• The first term (a) = 19.
• The common difference (d) = 16 - 19 = -3.

Since we have the find the term that is negative, it indicates that it is lesser than 0.

$\Longrightarrow \ \ \sf a_n\ <\ 0\\\\\\\implies\ a\ +\ (n \ -\ 1)d\ <\ 0\\\\\\\implies\ 19\ +\ (n\ -\ 1)(-3)\ <\ 0\\\\\\\implies\ 19\ -\ 3n\ +\ 3\ <\ 0\\\\\\\implies\ 22\ -\ 3n\ <\ 0\\\\\\\implies\ 22\ <\ 3n\\\\\\\implies\ \dfrac{22}{3}\ <\ n\\\\\\\implies\ 7.33\ <\ n$

Since it's lesser that n, n = 8.

Therefore, the 8th term of the AP is the first negative term.