Question

Арифметическая прогрессия задана условием b13=-3.2, bn+1=bn-4. Найти b16

Answer 1

B16=b15-5 b16=-15,2

Answer 2

Arithmetic Progression with Given Conditions

To find the value of b16 in the arithmetic progression defined by the conditions b13 = -3.2 and bn+1 = bn - 4, we can use the given information to determine the common difference (d) and the first term (a1) of the progression.

Let's start by finding the common difference (d). We know that bn+1 = bn - 4. Substituting n = 12 (since b13 = -3.2), we have:

b13+1 = b13 - 4 b14 = -3.2 - 4 b14 = -7.2

Therefore, the common difference (d) is -7.2 - (-3.2) = -4.

Next, we can find the first term (a1) of the arithmetic progression. We know that b13 = a1 + 12d. Substituting the values we have:

-3.2 = a1 + 12(-4) -3.2 = a1 - 48 a1 = -3.2 + 48 a1 = 44.8

Now that we have the common difference (d = -4) and the first term (a1 = 44.8), we can find b16 using the formula for the nth term of an arithmetic progression:

bn = a1 + (n - 1)d

Substituting n = 16, a1 = 44.8, and d = -4, we have:

b16 = 44.8 + (16 - 1)(-4) b16 = 44.8 + 15(-4) b16 = 44.8 - 60 b16 = -15.2

Therefore, b16 = -15.2.

Please let me know if there's anything else I can help you with!