Insert 6 numbers between – 6 and 29 such that the resulting sequence is an A.P.

Asked by Topperlearning User | 22nd Nov, 2017, 10:04: AM

Expert Answer:

Let A1, A2, A3, …, A6  be 6 arithmetic means between – 6 and 29 and common difference be d.

Total number of terms = 6 + 2 = 8
 
begin mathsize 12px style 8 to the power of th space term space of space an space straight A. straight P. space equals space 29
minus 6 plus 7 straight d equals 29
7 straight d equals 35
straight d equals 5
straight A subscript 1 equals negative 6 plus 5 equals negative 1
straight A subscript 2 equals negative 1 plus 5 equals 4
straight A subscript 3 equals 4 plus 5 equals 9
straight A subscript 4 equals 9 plus 5 equals 14
straight A subscript 5 equals 14 plus 5 equals 19
straight A subscript 6 equals 19 plus 5 equals 24 end style
Thus, the A.P. is – 6, – 1, 4, 9, 14, 19, 24, 29.

Answered by  | 22nd Nov, 2017, 12:04: PM