Question

Which term of the following series is 17.25?
\(-0.25, 0.25, 0.75, \dots\)

• A. \(34^{\text{th}}\)
• B. \(36^{\text{th}}\)
• C. \(31^{\text{st}}\)
• D. \(32^{\text{nd}}\)

Hint:

To quickly check divisibility by 0.5, simply double the numerator. \( \frac{x}{0.5} = 2x \).

Answer 1

The Correct Option is B

Step 1: Identify the Progression:
The series is \(-0.25, 0.25, 0.75, \dots\) Check the common difference \(d\): \[ d = 0.25 - (-0.25) = 0.50 \] \[ d = 0.75 - 0.25 = 0.50 \] This is an Arithmetic Progression (AP) with first term \(a = -0.25\) and \(d = 0.5\). Step 2: Use the AP Formula:
The \(n^{\text{th}}\) term \(T_n\) is given by: \[ T_n = a + (n-1)d \] We are given \(T_n = 17.25\). \[ 17.25 = -0.25 + (n-1)(0.5) \] Step 3: Solve for \(n\):
Add 0.25 to both sides: \[ 17.50 = (n-1)(0.5) \] Divide by 0.5 (which is equivalent to multiplying by 2): \[ n - 1 = 17.5 \times 2 \] \[ n - 1 = 35 \] \[ n = 36 \] The term is the \(36^{\text{th}}\) term.