Final answer:
The general term of the given geometric sequence is an = 4 * 0.275^(n-1). The 7th term (a7) can be found by substituting n=7 into the general term formula. The sum of the first 12 terms (S12) can be found using the formula Sn = a1 * (1 - r^n)/(1 - r).
Step-by-step explanation:
(a) The general term (the nth term, an):
In a geometric sequence, the nth term can be found using the formula: an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.
For this sequence, a1 = 4 and the common ratio, r, can be found by dividing the second term (1.1) by the first term (4): r = 1.1/4 = 0.275.
Therefore, the general term of the sequence is: an = 4 * 0.275^(n-1).
(b) a7, the 7th term of the sequence:
Using the general term formula, we can substitute n=7 to find the 7th term:
a7 = 4 * 0.275^(7-1)
= 4 * 0.275^6
≈ 0.2689.
(c) The sum of the first 12 terms, S12:
The formula to find the sum of the first n terms of a geometric sequence is: Sn = a1 * (1 - r^n)/(1 - r).
Substituting the given values, we can find the sum of the first 12 terms:
S12 = 4 * (1 - 0.275^12)/(1 - 0.275)
≈ 8.876.