If the 5th term of a geometric progression is 162 and the 8th term is 4374, find the (i) 1st three terms of the sequence; (ii) sum of the first 10 terms​

see explanation

Step-by-step explanation:

The nth term of a geometric progression is

= a₁

where a₁  is the first term and r the common ratio

Given a₅ = 162 and a₈ = 4374 , then

a₁ = 162 → (1)

a₁ = 4374 → (2)

Divide (2) by (1)

=

r³ = 27

r = = 3

Substitute r = 3 into (1) and solve for a₁

a₁ = 162

81a₁ = 162

a₁ = = 2

Then

a₂ = a₁ × 3 = 2 × 3 = 6

a₃ = a₂ × 3 = 6 × 3 = 18

The first 3 terms are 2, 6, 18

(ii)

The sum to n terms of a geometric progression is

= , then

=

     =

     = 59049 - 1

     = 59048

answer: standard form is ax^2 + bx + c = 0

step-by-step explanation:

standard form is ax^2 + bx + c = 0

(2x + 1)(x - 2) = 0

distribute to get into standard form

2x^2 - 4x + x - 2 = 0

2x^2 - 3x - 2 = 0

a = 2, b= -3, c = -2

a is your answer