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Find the sum of the first eight terms of the geometric sequence whose first term is -2.5 and ratio is 2.

Sagot :

adioabiola

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

  • and first term, a = -2.5

Therefore, we have;

  • S(8) = -2.5(1 + 2 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷)

  • S(8) = -2.5(255)

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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