The first term of the geometric sequence is a(1) = 7.
The nth term of a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Where:
a(1) = the first term
r = ratio
Parameter given in the problem:
a(5) = 112
Plug n = 5 into the formula
a(1) . r⁵⁻¹ = 112
a(1) . r⁴ = 112 ....... (1)
a(7) = 448
Plug n = 7 into the formula
a(7) = a(1) . r⁶
448 = a(1) . r⁶ ..... (2)
Divide (2) by (1)
448 : 112 = r⁶ : r⁴
4 = r²
Since r² = 4, then r⁴ = ( r² )² = 4² = 16.
Substitute r⁴ = 16 into equation (1):
a(1) . 16 = 112
a(1) = 112/16 = 7
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