The 8th and the 10th term of a geometric sequence are – 21 and - 189 respectively. What is the 2nd term of the sequence?
+128448 Let the 8th term = ar^7 where a = 1st term and r is the common ratio between terms
Likewise the 10th term = ar^9
So
ar^9 = - 189 (1)
ar^7 = -21 (2)
Divide (1) by (2) and we have that r^2 = 9 if terms are increasing negatives → r = 3
And
a(3)^9 = -189
a = -189 / 3^9 = -189/19683 = - 7/729
Second term = (-7/729) * 3 = -21/729 = -7/243
If the terms alternate signs then r = -3
So
a(-3)^9 = -189
a = 189/19683 = 7/729
And the second term becomes (7/729)(-3) = -7/243 (exactly the same !!! )
