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
5.4k views
in Arithmetic Progression by (22.8k points)
closed by

An A.P. has a property that the sum of the first ten terms is half the sum of the next ten terms. If the second term is 13, then the common difference is

(a) 3 

(b) 2 

(c) 5 

(d) 4

1 Answer

+1 vote
by (23.7k points)
selected by
 
Best answer

Answer : (b) 2

Sum of first 10 terms = \(\frac{1}{2}\) (Sum of next 10 terms)

⇒ S10\(\frac{1}{2}\) (S20 – S10) ⇒ 3S10 = S20 

⇒ 3 × \(\frac{1}{2}\)[2a + 9d] = \(\frac{1}{2}\)[2a + 19d]  \(\big[\because S_n = \frac{n}{2}[2a+(n-1)d]\big]\) 

⇒ 3(2a + 9d) = 2(2a + 19d) 

⇒ 6a + 27d = 4a + 38d 

⇒ 2a = 11d 

⇒ 2(13 + d) = 11d (∵ Second term = 13 and 13 – a = d) 

⇒ 26 – 2d = 11d 

⇒ 13d = 26 

d = 2.

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.

...