Question

Find the sum of the first seven terms of the geometric sequence series having the following information: 2-8+32- … +a n

Answer 1

Answer:

• 6554

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From the given information we can see:

• The first term is a = 2,
• Common ratio is r = - 4

Use the equation for the sum of the first n terms:

• Sₙ =  a(rⁿ - 1)/(r - 1)
• S₇ = 2((-4)⁷ - 1)/(-4 - 1) = 6554

Answer 2

Answer:

$S_7=6554$

Step-by-step explanation:

$\boxed{\begin{minipage}{7 cm}\underline{Sum of the first n terms of a geometric series}\\\\ S_n=\dfrac{a(1-r^n)}{1-r} \\\\where:\\\phantom{ww} \bullet a is the first term. \\ \phantom{ww} \bullet r is the common ratio.\\\end{minipage}}$

Given geometric series:

$2-8+32-...+a_n$

The first term (a) of the sequence is 2:

$\implies a=2$

To find the common ratio (r), divide consecutive terms:

$\implies r=\dfrac{a_2}{a_1}=\dfrac{-8}{2}=-4$

To find the sum of the first 7 terms, substitute the found values of a and r into the formula, along with n = 7:

$\implies S_7=\dfrac{2(1-(-4)^7)}{1-(-4)}$

$\implies S_7=\dfrac{2(1-(-16384))}{5}$

$\implies S_7=\dfrac{2(16385)}{5}$

$\implies S_7=\dfrac{32770}{5}$

$\implies S_7=6554$