The 1st,12th and the last term of an AP are 4,31.5 and 376.5 respectively. Determine the number of terms in series

150

Step-by-step 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.

where are the options?

step-by-step explanation:

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