The 2nd and 5th terms of a GP are -7 and 57 respectively.deduce the common ratio,the first term, the sum of the first five terms

since the two given terms are 3 terms apart,

r^3 = -57/7
so a = -7/∛(57/7) = -7∛(7/57)
S5 = a(r^5-1)/(r-1)

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Did you know?

Did you know that in a geometric progression (GP), the common ratio can be deduced by dividing any term by the previous term? In the given scenario, if the 2nd term is -7 and the 5th term is 57, we can divide the 5th term by the 2nd term to find the common ratio. The result is 57 divided by -7, which gives us -8 as the common ratio. Furthermore, did you know that the first term of a GP can be found by dividing any term by the common ratio raised to the power of its position in the progression? In this case, we divide the 2nd term (-7) by the common ratio raised to the power of 2, since it is the 2nd term. Calculating this, we get the first term as 56. Lastly, did you know that the sum of the first n terms in a GP can be calculated using the formula S = a * (1 - r^n) / (1 - r), where S is the sum, a is the first term, r is the common ratio, and n is the number of terms? Applying this formula, we can find the sum of the first five terms of the GP. Plugging in the values, we have S = 56 * (1 - (-8)^5) / (1 - (-8)). By evaluating this expression, we can determine the sum of the first five terms.