Find the term of terms in a gp

There are 7 terms in the GP

Step-by-step explanation:

In the geometric progression, there is a constant ratio between each two consecutive terms

The rule of the nth term of the geometric progression is

, where

∵ The first term = 5

∴ a = 5

∵ The last term =

∴ a(n) =

∵ The common ratio =

→ Substitute these values in the rule above to find n

∵   =  5 .

→ Divide both sides by 5

∴ =  

→ Let us find how many 3 in 729

∵ 729 ÷ 3 = 243 ÷ 3 = 81 ÷ 3 = 27 ÷ 3 = 9 ÷ 3 = 3 ÷ 3 = 1

∴ There are 6 three in 729

∴ 729 =

→ Let us find how many 4 in 4096

∵ 4096 ÷ 4 = 1024 ÷ 4 = 256 ÷ 4 = 64 ÷ 4 = 16 ÷ 4 = 4 ÷ 4 = 1

∴ There are 6 four in 4096

∴ 4096 =

∵   = =

∴   =  

∵ The bases are equal

∴ Their exponents are equal

∴ 6 = n - 1

→ Add 1 to both sides

∴ 6 + 1 = n - 1 + 1

∴ 7 = n

∴ There are 7 terms in the GP

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12.4, 12.387, 12.26, 12.252, 6.241, 6.2, 6.015, 6.009, 1.411, 1.2, 1.056, 1.007, 0.31,   0.13, 0.5, 0.04

step-by-step explanation:

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