Two terms between the 1st and the 4th in the given geometric sequence is 21 and 147.
The formula for the nth term in a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Where:
a(1) = first term
r = common ratio
Parameters given:
a(1) = 3
a(4) = 1029
Substitute n = 4 into the formula:
a(n) = a(1) . rⁿ⁻¹
a(4) = 3 . r³
1029 = 3 . r³
r³ = 1029/3 = 343
r = 7
Two terms between the 1st and the 4th term is a(2) and a(3).
In a geometric sequence, the following applies:
a(n) = a(n-1) . r
Hence,
a(2) = 3 . r
= 3 . 7 = 21
a(3) = a(2) . r
= 21 . 7 = 147
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