Sum 1-6

Find the sum of the geometric progression 3, 15, 75,… to six terms.

Correct answer:

s₆ =  11718

Step-by-step explanation:

$$\begin{gathered} a_1=3 \\ {a}_2=15 \\ r=a_2\mathrm{/}{a}_1=15\mathrm{/}3=5 \\ {s}_6=a_1\cdot {\displaystyle \frac{r^6-1}{r-1}}=3\cdot {\displaystyle \frac{5^6-1}{5-1}}=11718 \\ \text{ Verifying Solution: } \\ {a}_3=75 \\ {a}_4=r\cdot a_3=5\cdot 75=375 \\ {a}_5=r\cdot a_4=5\cdot 375=1875 \\ {a}_6=r\cdot a_5=5\cdot 1875=9375 \\ {S}_6=a_1+a_2+a_3+a_4+a_5+a_6=3+15+75+375+1875+9375=11718 \end{gathered}$$

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