the numbers log (a 3 b 7),log (a 5 b 12) and log (a 8 to b15) are the first thre

Question

the numbers log (a 3 b 7),log (a 5 b 12) and log (a 8 to b15) are the first three terms of anarithmetic progression of the 12th term is log (n b).what is thevalue of n?

Explanation / Answer

Look at the first three values of a that you aregiven:      a1 = 3      a2 = 5      a3 = 8      an = n + an-1 for n>1 So the first 12 values of a are    a1 = 3      a2 = a1 + 2 = 3 + 2 = 5      a3 = a2 + 3 = 5 + 3= 8    a4 = a3 + 4 = 8 + 4=12    a5 = a4 + 5 = 12 + 5 =17    a6 = a5 + 6 = 17 + 6 =23    a7 = a6 + 7 = 23 + 7 =30    a8 = a7 + 8 = 30 + 8 =38    a9 = a8 + 9 = 38 + 9 =47    a10 = a9 + 10 = 47 + 10 =57    a11 = a10 + 11 = 57 + 11= 68    a12 = a11 + 12 = 68 + 12= 80 a12 = n, so n = 80

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