Consider each given sequence start.

Question

i). Classify each as arithmetic, geometric, and/or none of these.

ii). Find the 28^th term.

iii). Find the sum of the first 7 terms, call it S₇.

a). 44,-6,44,-4,...

b). 3/4,3/2,3,6,... (3/4 and 3/2 are fractions, I just cannot write them like that because I do not have a special keyboard/program for it).

c). 88,83,78,73,...

d). x,3x-1,9x+2,27x-3,...

(Skip ii part, the 28^th term on part d).

Answer 1

Consider each given sequence start.

i). Classify each as arithmetic, geometric, and/or none of these.

ii). Find the 28th term.

iii). Find the sum of the first 7 terms, call it S7.

Hello Yuliya,

a). 44,-6,44,-4,...

i). none of these.

ii). The 28th term = - 22

iii). Find the sum of the first 7 terms: S₇ = 164

b). 3/4, 3/2, 3, 6, ...

i). Geometric

ii). The 28th term: Use A_n = A₁* r ^n-1 with common ratio r = 2, and A₁ = 3/4

A₂₈ = 3/4 * (2) ^28-1

A₂₈ = 100663296

iii). Find the sum of the first 7 terms: Use S_n = A₁*(1 - rⁿ)/(1 - r)

S₇ = 3/4*(1 - 2⁷)/(1 - 2)

S₇ = 3/4*(1 - 128)/(1 - 2)

S₇ = 3/4*( -127)/( -1 )

S₇ = 381/4

c). 88,83,78,73,...

i). Arithmetic

ii). Find the 28th term. Use: A_n = A₁ + (n - 1)d .... with common difference d = -5, A₁ = 88

A₂₈ = 88 + (28 - 1)(-5)

A₂₈ = 88 + (27)(-5)

A₂₈ = 88 - 135

A₂₈ = - 47

iii). Find the sum of the first 7 terms: Use S_n = (n/2)*(A₁ + A_n), and A₇ = 58 from A_n formula.

S₇ = (7/2)*(88 + 58)

S₇ = (7/2)*(146)

S₇ = 7 * 73

S₇ = 511

d). x,3x-1,9x+2,27x-3,...

(Skip ii part, the 28th term on part d).

i). none of these.

ii) SKIP

iii). Find the sum of the first 7 terms:

S₇ = x + 3x-1 + 9x+2 + 27x-3 + 81x+4 + 243x-5 + 729x+6

S₇ = 1093x + 3