Question

I need to know the next 7 terms of the sequences

Answer 1

Given:

a₁ = 2/5

a₂ = 4/5

Since the first 2 terms are given, let's determine the remaining 3 terms using the given formula:

`\text{ a}_n\text{ = a}_(n-2)\text{ }.\text{ a}_(n-1)`

We get,

For a₃,

`\text{ a}_3\text{ = a}_(3-1)\text{ }.\text{ a}_(3-2)\text{ = a}_1\text{ }.\text{ a}_2`
`\text{ a}_3\text{ = \lparen}(2)/(5))((4)/(5))\text{ = }(8)/(25)`

For a₄,

`\text{ a}_4\text{ = a}_(4-2)\text{ }.\text{ a}_(4-1)\text{ = a}_2\text{ }.\text{ a}_3`
`\text{ a}_4\text{ = \lparen}(4)/(5))((8)/(25))\text{ = }(20)/(125)\text{ = }(4)/(25)`

For a₅,

`\text{ a}_5\text{ = a}_(5-2)\text{ }.\text{ a}_(5-1)\text{ = a}_3\text{ }.\text{ a}_4`
`\text{ a}_5\text{ = \lparen}(8)/(25))((4)/(25))\text{ = }(32)/(625)`

Therefore, the first five terms of the sequence are the following:

`\text{ }(2)/(5)\text{ , }(4)/(5)\text{ , }(8)/(25)\text{ , }(4)/(25)\text{ , }(32)/(625)`

For another two terms.

For a₆,

`\text{ a}_6\text{ = a}_(6-2)\text{ }.\text{ a}_(6-1)\text{ = a}_4\text{ }.\text{ a}_5`
`\text{ a}_6\text{ = \lparen}(4)/(25))((32)/(625))\text{ = }(128)/(15,625)`

For a₇,

`\text{ a}_7\text{ = a}_(7-2)\text{ }.\text{ a}_(7-1)\text{ = a}_5\text{ }.\text{ a}_6`
`\text{ a}_7\text{ = \lparen}(32)/(625))((128)/(15,625))\text{ = }(4,096)/(9,765,625)`