Question

If $19^{th}$ term of a non-zero arithmetic progression (AP) is zero, then its ($49^{th}$ term) : ($29^{th}$ term) is ________.

• A. 2:1
• B. 4:1
• C. 1:3
• D. 3:1

Hint:

If one term is zero, express 'a' in terms of 'd' to solve ratios easily.

Answer 1

The Correct Option is D

Step 1: Concept
General term of an AP: $a_n = a + (n-1)d$.
Step 2: Analysis of given condition
$a_{19} = 0 \Rightarrow a + 18d = 0 \Rightarrow a = -18d$.
Step 3: Calculation of required terms
- $a_{49} = a + 48d = (-18d) + 48d = 30d$. - $a_{29} = a + 28d = (-18d) + 28d = 10d$.
Step 4: Ratio Calculation
Ratio $= a_{49} / a_{29} = 30d / 10d = 3 / 1 = 3:1$.
Final Answer:(D)