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Step-by-step explanation:
Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;
The sum of an arithmetic series is expressed as
n is the number of terms
a is the first term of the sequence
d is the common difference
Given parameters
n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2
Required
Sum of the first seven terms of the sequence
The sum of the nth term of the sequence will be;
The sigma notation will be expressed as . <em>The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.</em>
By taking <span>logarithmic of base 10
∴ </span><span>
∴ x log 4 = log 64
∴
∴ The correct choice is
</span><span>x = log base 10 of 64, all over log base 10 of 4</span>