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
1.7k views
in Arithmetic Progression by (44.5k points)
closed by

Find the number of terms of the A.P. 63, 60, 57, ... so that their sum is 693. Explain the double answer.

1 Answer

+1 vote
by (55.4k points)
selected by
 
Best answer

AP = 63, 60, 57,…

Here, a = 63, d = 60 – 63 = -3 and Sn = 693

We know that,

⇒ 1386 = n[129 – 3n]

⇒ 3n2 – 129n + 1386 = 0

⇒ n2 – 43n + 462 = 0

⇒ n2 – 22n – 21n + 462 = 0

⇒ n(n – 22) - 21(n – 22) = 0

⇒ (n – 21)(n – 22) = 0

⇒ n – 21 = 0 or n – 22 = 0

⇒ n = 21 or n = 22

So, n = 21 and 22

If n = 21, a = 63 and d = -3

a21 = 63 + (21 – 1)(-3)

a21 = 63 + 20 × -3

a21 = 63 – 60

a21 = 3

and If n = 22, a = 63 and d = -3

a22 = 63 + (22 – 1)(-3)

a22 = 63 + 21 × -3

a22 = 63 – 63

a22 = 0

Now, we will check at which term the sum of the AP is 693.

So, the terms may be either 21 or 22 both holds true.

We get the double answer because here the 22nd term is zero and it does not affect the sum.

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.

...