- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# If the $ 9^{\text {th }} $ term of an AP is zero, prove that its $ 29^{\text {th }} $ term is twice its $ 19^{\text {th }} $ term.

Given:

The \( 9^{\text {th }} \) term of an AP is zero.

To do:

We have to prove that its \( 29^{\text {th }} \) term is twice its \( 19^{\text {th }} \) term.

Solution:

Let $a$ be the first term and $d$ be the common difference.

This implies,

$a_{9}=a+(9-1)d$

$0=a+8d$

$a=-8d$........(i)

$a_{29}=a+(29-1)d$

$=a+28d$

$=-8d+28d$ [From (i)]

$=20d$.........(ii)

$a_{19}=a+(19-1)d$

$=a+18d$

$=-8d+18d$ [From (i)]

$=10d$........(iii)

Therefore,

$a_{29}=2(10d)$

$=2\times a_{19}$ [From (iii)]

Hence proved.

- Related Articles
- Find the \( 20^{\text {th }} \) term of the AP whose \( 7^{\text {th }} \) term is 24 less than the \( 11^{\text {th }} \) term, first term being 12.
- The $9^{th}$ term of an AP is $499$ and its $499^{th}$ term is $9$. Which of its term is equal to zero.
- The ratio of the \( 11^{\text {th }} \) term to the \( 18^{\text {th }} \) term of an AP is \( 2: 3 \). Find the ratio of the \( 5^{\text {th }} \) term to the 21 term
- If $(m + 1)$th term of an A.P. is twice the $(n + 1)$th term, prove that $(3m + 1)$th term is twice the $(m + n + 1)$th term.
- The $4^{th}$ term of an A.P. is zero. Prove that the $25^{th}$ term of the A.P. is three times its $11^{th}$ term.
- The $14^{th}$ term of an A.P. is twice its $8^{th}$ term. If its $6^{th}$ term is $-8$, then find the sum of its first $20$ terms.
- The sum of the \( 5^{\text {th }} \) and the \( 7^{\text {th }} \) terms of an AP is 52 and the \( 10^{\text {th }} \) term is 46 . Find the AP.
- In an AP five times of $5^{th}$ term is equal to ten times the $10^{th}$ term, show that its 15th term is zero.
- If $m$ times the $m^{th}$ term of an AP is equal to $n$ times its $n^{th}$ term. find the $( m+n)^{th}$ term of the AP.
- If sum of the \( 3^{\text {rd }} \) and the \( 8^{\text {th }} \) terms of an AP is 7 and the sum of the \( 7^{\text {th }} \) and the \( 14^{\text {th }} \) terms is \( -3 \), find the \( 10^{\text {th }} \) term.
- If the $n^{th}$ term of an AP is $\frac{3+n}{4}$, then find its $8^{th}$ term.
- The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1 . Find the \( 15^{\text {th }} \) term.
- Choose the correct answer from the given four options:Which term of the AP: \( 21,42,63,84, \ldots \) is 210 ?(A) \( 9^{\mathrm{th}} \)(B) \( 10^{\text {th }} \)(C) \( 11^{\text {th }} \)(D) \( 12^{\text {th }} \)
- Choose the correct answer from the given four options:If 7 times the \( 7^{\text {th }} \) term of an AP is equal to 11 times its \( 11^{\text {th }} \) term, then its 18 th term will be(A) 7(B) 11(C) 18(D) 0
- Choose the correct answer from the given four options:If the \( 2^{\text {nd }} \) term of an AP is 13 and the \( 5^{\text {th }} \) term is 25 , what is its \( 7^{\text {th }} \) term?(A) 30(B) 33(C) 37(D) 38

Advertisements