Question

Первый член арифметической прогрессии равен 360, а ее разность составляет -6. С какого номера члены этой прогрессии меньше 100?

Answer 1

$a_n=a_1+d(n-1)\\360-6(n-1)<100\\-6(n-1)<-260\\n-1>43.3\\n>44.3$

n=45

Answer 2

Arithmetic Progression Analysis

The first term of an arithmetic progression is 360, and the common difference is -6. We need to find the number of terms in this progression that are less than 100.

To find the number of terms less than 100, we can use the formula for the nth term of an arithmetic progression: nth term (Tn) = a + (n-1)d where: - a = first term - n = number of terms - d = common difference

We can rearrange this formula to find the number of terms (n) for which Tn < 100.

Calculation

Using the given values: - a = 360 - d = -6 - Tn < 100

We can solve for n: 360 + (n-1)(-6) < 100

Solving for n: 360 - 6n + 6 < 100 6n > 360 - 100 - 6 6n > 260 n > 260 / 6 n > 43.33

Since the number of terms must be a whole number, the number of terms less than 100 in this arithmetic progression is 43.

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