Question

Which term of the AP 117, 104, 91, 78,...… is its first negative term

Answer 1

Answer:

11th

Step-by-step explanation:

Let the first negative be nth term. In APs,

nth term = a + (n - 1)d

In the question, d = 104 - 117 = - 13

The first negative term must be the first term to be less than 0. (-ve no. are always less than 0).

=> nth term < 0

=> a + (n - 1)d < 0

=> 117 + (n - 1)(-13) < 0

=> 117 - 13n + 13 < 0

=> 130 < 13n

=> 10 < n

As n is greater than 10,n must be 11(as n€W).

11th term is the first negative term of this AP.

Answer 2

Step-by-step explanation:

ANSWER ______$✍️

Given sequence is 117, 104, 91, 78

First term (a) = 117

Common difference (d) = Second term – first term

• = 104 – 117
• = – 13

We know that, nth term = a + (n – 1)d

Then,

8th term = a + (8 – 1)d

• = 117 + 7(-13)
• = 117 – 91 = 26

∴ 8th term of the A. P. is 26

Hope this helps you