Question

If 14^th term of an A.P. is 4 and its 15^th term is zero, then its first term is ______.

Options

• –48

• –56

• 56

• 48

Answer 1

If 14^th term of an A.P. is 4 and its 15^th term is zero, then its first term is 56.

Explanation:

1. Set up the equations

The n^th term of an arithmetic progression is given by the formula:

T_n = a + (n – 1)d

where a is the first term and d is the common difference.

Based on the information provided:

The 14^th term is 4:

a + (14 – 1)d = 4 

⇒ a + 13d  = 4

The 15^th term is 0:

a + (14 – 1)d = 0 

⇒ a + 14d  = 0

2. Solve for the common difference

Subtract the first equation from the second:

(a + 14d) – (a + 13d) = 0 – 4

d = –4

3. Solve for the first term

Substitute the value of d back into one of the equations e.g., the second equation:

a + 14(–4) = 0

a – 56 = 0

a = 56