Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
78 views
in Arithmetic Progression by (238k points)
closed by
In an AP, the ratio of the fifth term to the eleventh term is 2 : 3. The sixth term is 13. Find the ratio of the eleventh term and the fifteenth term.
1. 8 : 11
2. 9 : 11
3. 11 : 9
4. 11 : 8

1 Answer

0 votes
by (240k points)
selected by
 
Best answer
Correct Answer - Option 2 : 9 : 11

Given:

In an AP, the ratio of the fifth term to the eleventh term is 2 : 3. The sixth term is 13.

Formula used:

nth term of an AP, Tn = a + (n - 1)d,

where ‘a’ is the first term, ‘n’ is the total number of terms and ‘d’ is the common difference.

Calculation:

Let the first term is ‘a’ and common difference is ‘d’.

According to question

T5/T11 = 2/3

⇒ (a + 4d)/(a + 10d) = 2/3

⇒ 3a + 12d = 2a + 20d

⇒ a – 8d = 0     ----(1)

And T6 = 13 (given)

⇒ a + 5d = 13     ----(2)

Solving equation (1) and (2)

8d + 5d = 13

⇒ 13d = 13

⇒ d = 1

and by putting value d = 1 in equation (1) we get,

a = 8

The ratio of the eleventh term and the fifteenth term = (a + 10d)/(a + 14d)

⇒ (8 + 10 × 1)/(8 + 14 × 1)

⇒ 18/22

∴ required answer is 9/11.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...