Question

Please help... AP is arithmetic progression

Answer 1

The least value of n is 17.

Explanation:

First term (a) = 46

Second term (a + d) = 43

Third term (a + 2d) = 40

Common difference (d) = second term - first term = 43 - 46 = -3

Tn (nth term) = a + (n - 1)d

a = 46, d = -3

Tn = 46 + (n - 1)-3 = 46 + (-3n + 3) = 46 - 3n + 3 = 49 - 3n

For Tn to be negative, the product of 3 and n must be greater than 49.

Therefore, the least value of n is 17

Answer 2

17

Explanation:

AP 46, 43, 40

a₁= 46, a₂= 43, a₃=40

d= a₃-a₂= a₂-a₁= -3

aₙ= 46+(n-1)*(-3)= 46-3n+3= 49- 3n

nth term is negative, so:

• aₙ<0 ⇒ 49-3n<0 ⇒ 3n>49 ⇒ n>49/3= 16 1/3 ⇒ n≥17

So the least n=17