Answer: 150
Explanation:
To solve arithmetic progression, the nth term is calculated using the formula = a + (n - 1)d
From the question,
First term = a = 4
12th term = 31.5
We need to get the common difference which will be:
Since 12th term = 31.5
a + (n - 1)d = 31.5
a + (12 - 1)d = 31.5
a + 11d = 31.5
Recall that a = 4
4 + 11d = 31.5.
11d = 31.5 - 4
11d = 27.5
d = 27.5 / 11
d = 2.5
Since last term is 376.5, the number of terms in it will be calculated as:
a + (n - 1)d = 376.5
4 + (n - 1)2.5 = 376.5
4 + 2.5n - 2.5 = 376.5
2.5n = 376.5 - 4 + 2.5
2.5n = 375
n = 375 / 2.5
n = 150
The number of terms in the series is 150.