Question

There are n AM's between 7 and 85 such that (n- 3)th mean: nth mean is 11:24, then find 'n'

Answer 1

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Answer 2

"Given there are m number of arithmetic means are inserted between 7 and 85

So, 7, a1 , a2 , a3 ,.....................an , 85 are in AP of n + 2 terms, Let d be the common difference

Total number of terms = n + 2

(n-3)th AM/ nth AM = 11/24

T(n+3) +1/ T (n+1) = 11/24

2 + (n-2-1)d/ 7 + (n+1-1)d = 11/24

7 +(n-3)78/n+1 divided by 7 + n7/(n+1) = 11/24

7n + 7 + 78n – 234/7n +7+78n = 11/24

85n-227/85n+7 = 11/24

204n – 5448 = 935n +77

1105n = 5525

N = 5

"