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
1.0k views
in Arithmetic Progression by (20 points)
edited by

How many terms of the series 42+39+36+... makes the sum 315? 

Please log in or register to answer this question.

1 Answer

0 votes
by (18.1k points)

Given series is S = 42+39+36+...

Let first term of the sequence is a1 = a = 42.

Common difference of the sequence is d = a2 - a1 = 39 - 42 = -3.

∴ Sum of n terms of the sequence is Sn = n/2 [2a+(n-1)d]

Given that sum = 315

∴ n/2 [2 x 42 + (n-1) x -3] = 315

⇒ 42n -3/2 n(n-1) = 315

⇒ 84n - 3n2 + 3n = 630

⇒ 3n2 - 87n + 630 = 0

⇒ n2 - 29n + 210 = 0

⇒ n2 - 14n - 15n + 210 = 0

⇒ (n - 14) (n - 15) = 0

⇒ n = 14 or n = 15

Hence, sum of 14th terms of the series is 315. Also, sum of 15th terms is 315 (∵ a15 = a+14d = 0)

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.

...