Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 47
For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $$(n + 2n^2)$$. If the $$n^{th}$$ term of the progression is divisible by 9, then the smallest possible value of n is
Solution
It is given,
$$S_n=2n^2+n$$
$$S_{n-1}=2\left(n-1\right)^2+\left(n-1\right)$$
$$S_{n-1}=2n^2-3n+1$$
$$T_n=S_n-S_{n-1}=2n^2+n-2n^2+3n-1=4n-1$$
$$T_n=4n-1$$
The terms are 3, 7, 11, 15, 19, 23, 27,......
27 is the first term in the series divisible by 9.
27 is the 7th term.
Therefore, the least possible value of n is 7.
The answer is option C.
Video Solution
Your Doubts
Ask a Doubt
(know more)
Drop Your File Here!
Ask Your Doubt
Drop Your File Here!
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 Functions, Graphs and Statistics QuestionsCAT Percentages QuestionsCAT Venn Diagrams QuestionsCAT Time Speed Distance QuestionsCAT Time And Work Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Venn Diagrams QuestionsCAT Data Interpretation Basics QuestionsCAT Arrangement QuestionsCAT Miscellaneous LR QuestionsCAT DI with connected data sets Questions
