The sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2 is: -637.5
The nth term of a geometric sequence is given mathematically as;
T(n) = ar^n
- where, a = first term of the geometric sequence.
- r = common ratio of the sequence
- and n = nth term of the sequence.
Therefore, the sum of the first 8 terms of the geometric sequence is;
- S(8) = a + ar + ar² + ar³ + ar⁴ + ar⁵ + ar⁶ + ar⁷.
In essence;
- since common ratio, r = 2
Therefore, we have;
- S(8) = -2.5(1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)
S(8) = -637.5.
Therefore, the sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2 is: -637.5
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