Question

Арифметическая прогрессия 1.а6=49а20=7S12-?--------------------------------------------------------------------2. а1=8а10=44s25-?

Answer 1

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Answer 2

To find the missing terms in the arithmetic progressions, we need to determine the common difference (d) between consecutive terms. Once we know the common difference, we can easily find any term in the arithmetic progression.

1. а6 = 49 and а20 = 7

Let's find the common difference (d) using the formula for the nth term of an arithmetic progression:

a_n = a_1 + (n - 1) * d

Where: a_n = the nth term a_1 = the first term n = the term number d = common difference

We have two equations using the given terms: a_6 = a_1 + 5d = 49 ........(1) a_20 = a_1 + 19d = 7 ......(2)

Now, we can solve these two equations simultaneously to find the values of a_1 and d.

Subtracting equation (2) from equation (1):

(a_1 + 5d) - (a_1 + 19d) = 49 - 7 -14d = 42 d = -3

Now that we have the common difference (d = -3), we can find the missing term а12.

a_12 = a_1 + (12 - 1) * (-3) a_12 = a_1 - 33

However, we don't have enough information to determine the exact value of a_1, so we cannot find the value of а12 at this point.

2. а1 = 8 and а10 = 44

Using the same formula as above, we'll find the common difference (d) using the two given terms:

a_1 = a_1 + 0 * d = 8 ........(1) a_10 = a_1 + 9d = 44 ......(2)

Subtracting equation (1) from equation (2):

(a_1 + 9d) - (a_1) = 44 - 8 9d = 36 d = 4

Now that we have the common difference (d = 4), we can find the missing term а25.

a_25 = a_1 + (25 - 1) * 4 a_25 = a_1 + 96

Again, we don't have enough information to determine the exact value of a_1, so we cannot find the value of а25 at this point.

In both cases, we are missing information about the initial term (a_1) to compute the missing term in the arithmetic progressions. Without knowing the value of a_1, we cannot find the specific terms а12 and а25.