Question

Find the number of terms in an ap given that its first and last terms are a and 37 a respectively and that its common differences is 4a.

a) 6 terms
b) 9 terms
c) 12 terms
d) 15 terms

Answer 1

The arithmetic progression series with a first term of 'a', a last term of '37a', and a common difference of '4a' has 10 terms. None of the provided options matches this answer, suggesting there may be an error in the question.

Step-by-step explanation:

To find the number of terms in an arithmetic progression (AP), we can use the formula for the nth term which is:

Tn = a + (n - 1)d

Where Tn is the last term, a is the first term, n is the number of terms, and d is the common difference. In this case, the last term is given to be 37a and the common difference is provided as 4a.

Substituting the given values into the formula we get:
37a = a + (n - 1) * 4a

This simplifies to:
36a = (n - 1) * 4a
9 = n - 1
n = 10

The AP series has 10 terms, which is not one of the options provided (a-d). Therefore, it appears there might be a mistake in the given options or in the values stated in the question.