In GP n-th term:
an = a • r ⁿ⁻¹
where
a = a1 = initial value
r = common ratio
In this case:
a4 = 3 / 7
a4 = a • r ³
a • r ³ = 3 / 7
a7 = a • r ⁶
a7 = 8 • a4 = 8 • 3 / 7 = 24 / 7
a7 / a4 = a • r ⁶ / a • r ³ = r ³
( 24 / 7 ) / ( 3 / 7 ) = 24 / 3 = 8 = r ³
r = ∛8
r = 2
Put this value in equation:
a • r ³ = 3 / 7
a • 2 ³ = 3 / 7
8 a = 3 / 7
a = ( 3 / 7 ) / 8 = 3 / 7 • 8
a = 3 / 56
a3 = a • r ² = 3 / 56 • 2² = 3 / 56 • 4 =
12 / 56 = 4 • 3 / 4 • 14 = 3 / 14
The 4th term of a GP is 3/7.If the 7th term is eight times as much as the 4th term, find the third term of the progression.
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