Question

if the fourth term of an ap is 0, then a25/a11=​

Answer 1

Given :-

• If the fourth term of $\sf a_p$ is 0
• $\sf a_p = 0$

To Find :-

• Find the value of $\sf \frac{a_25}{a_11}$

Answer :-

• $\sf \red{3}$

Explanation :-

• For $\sf 4th$ term,

• $\sf a_4 = a + 3d = 0$
• $\sf a + 3d = 0$

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• For $\sf 11th$ term

• $\sf a_11 = a + 3d$
• $\sf = a + 10d$
• $\sf = (a + 3d )+ 7d$
• $\sf = 0 + 7d$ [ we know a + 3d = 0 ]
• $\sf = \red{7d}$

_________________

• For $\sf 25th$

• $\sf a_25 = a + 24d$
• $\sf = (a + 3d) + 21d$
• $\sf = 0 + 21 d$
• $\sf = \red{21d }$

Now get to the point,

$\sf \frac{a_25}{a_11}$

$\sf = \frac{21d}{7d}$

$\sf = \frac{\cancel{21d}^{\: \: 3}}{\cancel{7d}}$

$\sf = \fbox{ \red{3} }$

I hope it helps you ❤️✔️