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
2.0k views
in Arithmetic Progression by (55.4k points)
closed by

Three numbers are in A.P. Their sum is 27 and the sum of their squares is 275. Find the numbers.

1 Answer

+1 vote
by (44.5k points)
selected by
 
Best answer

Let the three numbers are in AP = a, a + d, a + 2d

According to the question,

The sum of three terms = 27

⇒ a + (a + d) + (a + 2d) = 27

⇒ 3a + 3d = 27

⇒ a + d = 9

⇒ a = 9 – d …(i)

and the sum of their squares = 275

⇒ a2 + (a + d)2 + (a + 2d)2 = 275

⇒ (9 – d)2 + (9)2 + ( 9 – d + 2d)2 = 275 [from(i)]

⇒ 81 + d2 – 18d + 81 + 81 + d2 + 18d = 275

⇒ 243 + 2d2 = 275

⇒ 2d2 = 275 – 243

⇒ 2d2 = 32

⇒ d2 = 16

⇒ d = √16

⇒ d = ±4

Now, if d = 4, then a = 9 – 4 = 5

and if d = – 4, then a = 9 – ( – 4) = 9 + 4 = 13

So, the numbers are →

if a = 5 and d = 4

5, 9, 13

and if a = 13 and d = – 4

13, 9, 5

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.

...