Question

Find the 10^th term of the arithmetic progression \(5,1,-3,-7,..….\)

• A. 31
• B. -31
• C. 30
• D. -30

Answer 1

The Correct Option is B

1. The given arithmetic progression (A.P.) is:

5, 1, −3, −7, . . .

2. The general form of an A.P. is:

The nth term \( a_n \) of an A.P. is given by:

\( a_n = a_1 + (n-1) \cdot d \)

Where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

3. Finding the common difference:

The common difference \( d \) is the difference between any two consecutive terms:

\( d = 1 - 5 = -4 \)

4. Finding the 10th term:

Substitute \( a_1 = 5 \), \( d = -4 \), and \( n = 10 \) into the formula:

\( a_{10} = 5 + (10-1) \cdot (-4) \)

\( a_{10} = 5 + 9 \cdot (-4) \)

\( a_{10} = 5 - 36 \)

\( a_{10} = -31 \)