Find explicit formula that generates a sequence whose first four terms are 23, 17, 11, 5.

We can see that the ratio is 17/23, and the initial value a(1) is 23. Therefore we can create this formula: f(x) = 23(17/23)^x-1 or [tex]c, l_{n} = 23-6n[/tex]

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keshavgandhi04 keshavgandhi04 · Answer 2 · 2022-08-03T09:37:57+02:00

The explicit formula (nth term) for the arithmetic progression of the given AP 23, 17, 11, 5 will be 29 - 6n so option (D) will be correct.

What is Arithmetic progression?

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2 .

Given that an Arithmetic progression 23, 17, 11, 5.

The common difference d = 17 - 23 = -6

The formula for the nth term in AP is [tex]a_{n}[/tex] = a + (n - 1)×d where a is the first term and n is a number of terms.

[tex]a_{n}[/tex] = 23 + (n -1) × (-6) = 29 - 6n hence it will be correct answer.

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Find explicit formula that generates a sequence whose first four terms are 23, 17, 11, 5.​

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What is Arithmetic progression?

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Find explicit formula that generates a sequence whose first four terms are 23, 17, 11, 5.