Step-by-step explanation:
Consider the following sequence:
![a_n=a(n)=2n\text{ -1}](https://img.qammunity.org/2023/formulas/mathematics/college/eeswkey0paqepqdj3tlxcnw1e5s9xwbsxt.png)
If we evaluate this sequence for each first six natural numbers (starting from 1), we get the following:
for n= 1
![a_{1\text{ }}=a(1)\text{ = 2\lparen1\rparen-1 = 2-1 = 1}](https://img.qammunity.org/2023/formulas/mathematics/college/44p6egpexzz44gow94biqyxcb7cgwd9mhk.png)
for n= 2
![a_2=\text{ a\lparen2\rparen= 2\lparen2\rparen-1 = 4-1 = 3}](https://img.qammunity.org/2023/formulas/mathematics/college/nab01zca68a4h473na607nsnt6dxtikyd3.png)
for n = 3:
![a_3=\text{ a\lparen3\rparen= 2\lparen3\rparen-1 = 6-1 = 5}](https://img.qammunity.org/2023/formulas/mathematics/college/p4hfyfpxysze2dpbh1qgvgxmt9p7f65ctc.png)
for n= 4:
![a_4=\text{ a\lparen4\rparen=2\lparen4\rparen-1 = 8-1 = 7}](https://img.qammunity.org/2023/formulas/mathematics/college/yklby7scbmys9ibfai859p2nj6najn1ggk.png)
for n= 5:
![a_5=\text{ a\lparen5\rparen=2\lparen5\rparen-1 = 10-1 = 9}](https://img.qammunity.org/2023/formulas/mathematics/college/6k24765heb8gfmmwew1ai4jv9tm4wuz1hn.png)
and for n= 6:
![a_{6\text{ }}=\text{ a\lparen6\rparen= 2\lparen6\rparen-1 = 12-1 = 11}](https://img.qammunity.org/2023/formulas/mathematics/college/ww93ome03dqtj8xudghwhmmdlgbynxaqfz.png)
we can conclude that the correct answer is:
Answer:
![a_{1\text{ }}=\text{ 1}](https://img.qammunity.org/2023/formulas/mathematics/college/pirkc8h5f9xbbtcetzqmsx48a9omar8w8d.png)
![a_2=\text{ 3}](https://img.qammunity.org/2023/formulas/mathematics/college/tp7yh7v3tl1cog6r0z2p3e18cw7fn0v3tb.png)
![a_3=\text{ 5}](https://img.qammunity.org/2023/formulas/mathematics/college/7mepmk9oetz6r6jo86rqxc1vk04xljcm0k.png)
![a_4=\text{ 7}](https://img.qammunity.org/2023/formulas/mathematics/college/xhizdpucr3plqmk2skn6351hnu39injf4w.png)
![a_5=\text{ 9}](https://img.qammunity.org/2023/formulas/mathematics/college/gle7mt9zn3gjvc3w163j3503j62es383no.png)
![a_{6\text{ }}=\text{ 11}](https://img.qammunity.org/2023/formulas/mathematics/college/nxzuku3214aeuc3wkg8xou3q9p7oyniii9.png)