Calculate a_57 for the sequence {a_n}={-6,- 9/2,-3,- 3/2,0}

Answer 1

To find the value of a_57, we need to see if there is a pattern in the sequence. Looking at the sequence, we can see that each term increases by 3/2:

-6, -9/2, -3, -3/2, 0

Next, we need to determine how many times the sequence increases by 3/2 to reach a_57. We can do this by finding the difference between a_1 and a_57 and dividing it by the common difference (3/2).

a_1 = -6
a_57 = ?

a_57 - a_1 = 56 * (3/2) = 42

So, a_57 = a_1 + 42 * (3/2)

a_57 = -6 + 42 * (3/2)

a_57 = -6 + 63/2

a_57 = -6 + 31.5

a_57 = 25.5

Therefore, a_57 = 25.5.