Find the 20th term of the following sequence. -6, -4, -2, 0, ... 32 44 46
2 answers:
Answer:
20th term should be 32.
Step-by-step explanation:
The given sequence is -6, -4, -2, 0,.......32, 44, 46
In this sequence we can say that there is a common difference = -4 + 6 = 2 = (T₂ - T₁)
Therefore, the sequence is an arithmetic sequence.
Now explicit formula of an arithmetic sequence is given by
= a+ ( x - 1 ) d
Here a = first term
n = number of term
d = common difference
For the 20th term of the sequence.
= -6 + ( 20 - 1 ) 2
= -6 + 19 × 2
= 38 - 6
= 32
Therefore, 20th term should be 32.
You might be interested in
1. The function 
is a parabola of the form 
. The the formula for the axis of symmetry of a parabola is 
. We can infer from our function that 
and 
, so lets replace those values in our formula:
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
or 
or 
From our previous point we know that the ball reaches its maximum time at
, which means that <span>it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.</span>
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
From our previous point we know that the ball reaches its maximum time at