# Math

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

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1. 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

7 / 2 , - 7 , 14 , - 28 , 56...

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2. Please what is the square for

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