Asked by Faith
The 2nd and 5th terms of a GP are -7 and 56 respectively. Find:
a. The common ratio
b. The first term
c. The sum of the first five terms
a. The common ratio
b. The first term
c. The sum of the first five terms
Answers
Answered by
Bosnian
a2 = - 7 , a5 = 56
nth term in GP:
an = a1 ∙ r ⁿ⁻¹
where:
a1 = first term , r = common ratio
a2 = a1 ∙ r ²⁻¹ = r¹ = a1 ∙ r
a5 = a1 ∙ r ⁵⁻¹ = a1 ∙ r ⁴
a5 = a1 ∙ r ∙ r ³
a5 = a2 ∙ r ³
56 = ( - 7 ) ∙ r ³
Divide both sides by - 7
56 / ( - 7 ) = r ³
- 8 = r ³
r ³ = - 8
r = ∛ - 8
r = - 2
a2 = a1 ∙ r
- 7 = a1 ∙ ( - 2 )
Divide both sides by - 2
- 7 / - 2 = a1 ∙ ( - 2 ) / - 2
7 / 2 = a1
a1 = 7 / 2
The sum of the n terms in GP:
Sn = a1 ∙ ( 1 - rⁿ ) / ( 1 - r )
The sum of the first five terms:
S5 = a1 ∙ ( 1 - r⁵ ) / ( 1 - r )
S5 = ( 7 / 2 ) ∙ [ 1 - ( - 2⁵ ) ] / [ 1 - ( - 2 ) ]
S5 = ( 7 / 2 ) ∙ [ 1 - ( - 32 ) ] / ( 1 + 2 )
S5 = ( 7 / 2 ) ∙ ( 1 + 32 ) / 3
S5 = ( 7 / 2 ) ∙ 33 / 3
S5 = ( 7 / 2 ) ∙ 11
S5 = 77 / 2 = 38.5
Your GP:
7 / 2 , - 7 , 14 , - 28 , 56...
nth term in GP:
an = a1 ∙ r ⁿ⁻¹
where:
a1 = first term , r = common ratio
a2 = a1 ∙ r ²⁻¹ = r¹ = a1 ∙ r
a5 = a1 ∙ r ⁵⁻¹ = a1 ∙ r ⁴
a5 = a1 ∙ r ∙ r ³
a5 = a2 ∙ r ³
56 = ( - 7 ) ∙ r ³
Divide both sides by - 7
56 / ( - 7 ) = r ³
- 8 = r ³
r ³ = - 8
r = ∛ - 8
r = - 2
a2 = a1 ∙ r
- 7 = a1 ∙ ( - 2 )
Divide both sides by - 2
- 7 / - 2 = a1 ∙ ( - 2 ) / - 2
7 / 2 = a1
a1 = 7 / 2
The sum of the n terms in GP:
Sn = a1 ∙ ( 1 - rⁿ ) / ( 1 - r )
The sum of the first five terms:
S5 = a1 ∙ ( 1 - r⁵ ) / ( 1 - r )
S5 = ( 7 / 2 ) ∙ [ 1 - ( - 2⁵ ) ] / [ 1 - ( - 2 ) ]
S5 = ( 7 / 2 ) ∙ [ 1 - ( - 32 ) ] / ( 1 + 2 )
S5 = ( 7 / 2 ) ∙ ( 1 + 32 ) / 3
S5 = ( 7 / 2 ) ∙ 33 / 3
S5 = ( 7 / 2 ) ∙ 11
S5 = 77 / 2 = 38.5
Your GP:
7 / 2 , - 7 , 14 , - 28 , 56...
Answered by
CONFIDENCE
Please what is the square for
Answered by
Sammylin
Alphabet B
2nd term=-7
5th term=56
r=-2
Substitute -2 for r in (1)
a=-7
a=1.75
2nd term=-7
5th term=56
r=-2
Substitute -2 for r in (1)
a=-7
a=1.75
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