Question

Найти порядковый номер числа 110 в арифметической прогрессии 10 14 18​

Answer 1

Ответ:

26

Объяснение:

$(a_n)\; 10;14;18;...110;...\\\\a_n=110\\n=?\\\\a_1=10,\; a_2=14\\d=a_2-a_1=14-10=4\\\\a_n=a_1+d(n-1)\\a_n=110\\\\10+4(n-1)=110\\4(n-1)=100\\n-1=25\\n=26$

$110=a_{26}$

Answer 2

Finding the Position of 110 in an Arithmetic Progression

To find the position of the number 110 in the arithmetic progression 10, 14, 18, we can use the formula for the nth term of an arithmetic progression:

nth term (Tn) = a + (n-1)d

Where: - a = first term of the progression - n = position of the term we want to find - d = common difference between the terms

In this case: - a = 10 - d = 14 - 10 = 4 - We want to find the position of 110, so Tn = 110

Using the formula, we can solve for n:

110 = 10 + (n-1) * 4

110 = 10 + 4n - 4

110 = 6 + 4n

4n = 110 - 6

4n = 104

n = 104 / 4

n = 26

So, the position of the number 110 in the arithmetic progression 10, 14, 18 is 26.