Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
a)write an inequality to find the three numbers. let n represent the smallest even number.
b)solve the inequality

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Ответ:

Skylynn11

04.12.2022

Mathematics

(a)

$T_n = 3(-4)^{n-1}$

(b)

$\sum\limits^n_1 { 3(-4)^{n-1}$

Step-by-step explanation:

Given

The above sequence

Solving (a): The explicit formula

The given sequence is a geometric sequence because the common ratio (r) is:

$r = \frac{-12}{3} = \frac{48}{-12} = \frac{-192}{48} = \frac{768}{-192}$

r = -4

The explicit formula is calculated using the n term of an GP.

$T_n = ar^{n-1}$

$T_n = 3 * (-4)^{n-1}$

$T_n = 3(-4)^{n-1}$

Solving (b): Summation notation.

This implies that the sum of the sequence.

To do this, we write Tn inside the summation sign

i.e.

$\sum\limits^n_1 {T_n}$

Substitute values for Tn

$\sum\limits^n_1 { 3(-4)^{n-1}$

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Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. a)write an inequality to find the three numbers. let n represent the smallest even number. b)solve the inequality