Question

Tenth term of the AP \( 1, -1, -3, -5, \dots \) is

• A. \( -15 \)
• B. \( -17 \)
• C. \( -13 \)
• D. \( -10 \)

Hint:

The \( n^{th} \) term of an AP with first term \( a_1 \) and common difference \( d \) is \( a_n = a_1 + (n - 1)d \).

Answer 1

The Correct Option is B

Step 1: Identify the first term and the common difference.
In the given arithmetic progression \( 1, -1, -3, -5, \dots \), the first term is \( a_1 = 1 \). The common difference \( d \) is the difference between consecutive terms: \[ d = a_2 - a_1 = -1 - 1 = -2 \] We can verify this: \[ d = a_3 - a_2 = -3 - (-1) = -3 + 1 = -2 \] Step 2: Use the formula for the \( n^{th} \) term of an AP.
The \( n^{th} \) term of an arithmetic progression is given by the formula: \[ a_n = a_1 + (n - 1)d \] We need to find the tenth term, so \( n = 10 \). Step 3: Substitute the values into the formula. \[ a_{10} = a_1 + (10 - 1)d \] \[ a_{10} = 1 + (9)(-2) \] \[ a_{10} = 1 - 18 \] \[ a_{10} = -17 \] The tenth term of the arithmetic progression is \( -17 \).