Calculate a_57 for the sequence {a_n}={-6,-9/2,-3,-3/2,0}
common difference is +3/2 but how do i find the 57th term?

the 57th term is 78

Step-by-step explanation:

The sequence is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 6

d =3/2

n = 57

We want to determine the value if the 57th term, T57. Therefore,

T57 = - 6 + (57 - 1) ×3/2

T57 = - 6 + 56 × 3/2 = - 6 + 84

T57 = 78