# The sum of the 2nd and the 7th term of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.

Let a be the first term and d be the common difference of the AP.

Given: a2 + a7 = 30

Also, a15 = 2a8 - 1

Consider a2 + a7 = 30

(a + d) + (a + 6d) = 30

2a + 7d = 30 ……………….. (1)

Consider a15 = 2a8 - 1

a + 14d = 2(a + 7d) - 1

a + 14d = 2a + 14d - 1

a = 1

First term = a = 1

Thus, from equation (1), we get,

7d = 30 - 2a

7d = 30 - 2

7d = 28

d = 4

Thus, the AP is a, a + d, a + 2d, a + 3d,…

Therefore, the AP is 1, 5, 9, 13, 17,…

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Lets Check Your Knowledge in A.P.49 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Quiz on Arithmetic Progression Quiz32 mins
Arithmetic Progression Tricks and QUIZ37 mins
Quiz | Group of Questions on General Term of an A.P49 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Become a Master of A.P. in 45 Minutes!!47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses