calculate a57 for the sequence {an}={-6,-9/2,-3,-3/2,0...}
The given sequence {an} can be written as:
{-6, -9/2, -3, -3/2, 0, ...}
We can see that the sequence is decreasing by 3/2 each time.
To find a57, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where:
an = nth term of the sequence
a1 = first term of the sequence
n = number of terms
d = common difference
For the given sequence, a1 = -6 and d = -3/2. Plugging in these values, we can calculate a57:
a57 = -6 + (57 - 1)(-3/2)
= -6 + 56(-3/2)
= -6 + (-84)
= -6 - 84
= -90
Therefore, a57 = -90.