Question 97

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

Name: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is
Uploaded: July 3, 2020, 10:14 a.m.
Duration: 1 min 53 s
Description: If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

Solution

The seventh term of an AP = a + 6d. Third term will be a + 2d and second term will be a + 16d. We are given that
$$ (a + 6d)^2 = (a + 2d)(a + 16d)$$
=> $$ a^2 $$ + $$36d^2$$ + 12ad = $$ a^2 + 18ad + 32d^2 $$
=> $$4d^2 = 6ad$$
=> $$ d:a = 3:2$$
We have been asked about a:d. Hence, it would be 2:3

Share on Whatsapp Share on Whatsapp

Boost your CAT prep: Take All-India 3 free CAT mock tests with Video solutions

Video Solution

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
38+ CAT previous year papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Linear Equations Questions CAT Mensuration Questions CAT Time And Work Questions CAT Logarithms Questions CAT Percentages Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Venn Diagrams Questions CAT Puzzles Questions CAT Games and Tournamnents Questions CAT Data Interpretation Questions CAT Truth Lie Concept Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Vocabulary Questions CAT Para Jumbles Questions CAT Verbal Ability Questions CAT Critical Reasoning Questions CAT Reading Comprehension Questions

Also Read

CAT Mock Tests

CAT 2025 Course

Free CAT Preparation

CAT Questions

CAT Formulas PDF

CAT Study Material

CAT Score vs Percentile

CAT Score Calculator

CAT Percentile Predictor

CAT Sectional Tests

CAT Exam

CAT Prep Videos

CAT Registration

CAT Syllabus 2025

CAT Eligibility Criteria

CAT Admit Card

CAT 2017 QA Slot 1 Question

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

Video Solution

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Also Read

Free CAT Quant Questions

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account

Get Started with 5000+ Free CAT Questions & Mock Tests with Detailed Solutions!