Question

A) a15 = 23 и d= - 3 b) a33 =7 1/16 и d= 5/16 c) a19 = 13 и a20 = 11

Answer 1

Ответ:

Пошаговое объяснение:

a)     a₁₅=23      d=-3     a₁=?

a₁₅=a₁+14*d

a₁+14*(-3)=23

a₁-42=23

a₁=65.

b) a₃₃=7¹/₁₆      d=⁵/₁₆     a₁=?

a₃₃=a₁+32*d

a₁+32*(5/16)=7¹/₁₆

a₁+(160/16)=113/16

a₁=-47/16

a₁=-2¹⁵/₁₆.

c) a₁₉=13     a₂₀=11     a₁=?

d=a₂₀-a₁₉=11-13=-2

a₁₉=a₁+18*d

a₁+18*(-2)=13

a₁-36=13

a₁=49.

Answer 2

Ответ: а) а1=а15-14*d=23+14*3=23+42=65.

В) а1=а33-32*d=7 1/16-32*5/16=(112-160)/16=-48/16=-3.

С) d=11-13=-2, а1=а19-18*d=13-18*(-2)=13+36=50.

Пошаговое объяснение:

Answer 3

To solve the given arithmetic sequences, we can use the formulas:

a_n = a_1 + (n - 1) * d

where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.

a) Given a_15 = 23 and d = -3, we can find a_1 as follows:

a_15 = a_1 + (15 - 1) * (-3) 23 = a_1 + 14 * (-3) 23 = a_1 - 42 a_1 = 23 + 42 a_1 = 65

So, the first term (a_1) for the sequence is 65.

b) Given a_33 = 7 1/16 and d = 5/16, we can find a_1 as follows:

a_33 = a_1 + (33 - 1) * (5/16) 7 1/16 = a_1 + 32 * (5/16) 7 1/16 = a_1 + 160/16 7 1/16 = a_1 + 10 a_1 = 7 1/16 - 10 a_1 = -2 15/16

So, the first term (a_1) for the sequence is -2 15/16.

c) Given a_19 = 13 and a_20 = 11, we can find d as follows:

a_20 = a_19 + (20 - 19) * d 11 = 13 + d d = 11 - 13 d = -2

So, the common difference (d) for the sequence is -2.