Joeyoman
17.11.2019 •
Mathematics
Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104. so i have to find r. but is this right: 7104 = 444r^4 r^4 = 16 r = 2 or should it be r^3? i'm never sure if the power is = the number of terms missing or something completely unrelated.
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Ответ:
Third term = t3 = ar^2 = 444 eq. (1)
Seventh term = t7 = ar^6 = 7104 eq. (2)
By solving (1) and (2) we get,
ar^2 = 444
=> a = 444 / r^2 eq. (3)
And ar^6 = 7104
(444/r^2)r^6 = 7104
444 r^4 = 7104
r^4 = 7104/444
= 16
r2 = 4
r = 2
Substitute r value in (3)
a = 444 / r^2
= 444 / 2^2
= 444 / 4
= 111
Therefore a = 111 and r = 2
Therefore t6 = ar^5
= 111(2)^5
= 111(32)
= 3552.
Therefore the 6th term in the geometric series is 3552.
Ответ: