Sure, let's solve this question step by step.
We need to create a sequence of numbers starting from 3, where each subsequent number in the sequence is obtained by adding 7 to the previous one. We want to find the first 10 numbers in this sequence.
1. Start with 3:
- The first number in the sequence is 3.
2. Add 7 to the previous number to get the next number:
- Second number: [tex]\( 3 + 7 = 10 \)[/tex]
- Third number: [tex]\( 10 + 7 = 17 \)[/tex]
- Fourth number: [tex]\( 17 + 7 = 24 \)[/tex]
- Fifth number: [tex]\( 24 + 7 = 31 \)[/tex]
- Sixth number: [tex]\( 31 + 7 = 38 \)[/tex]
- Seventh number: [tex]\( 38 + 7 = 45 \)[/tex]
- Eighth number: [tex]\( 45 + 7 = 52 \)[/tex]
- Ninth number: [tex]\( 52 + 7 = 59 \)[/tex]
- Tenth number: [tex]\( 59 + 7 = 66 \)[/tex]
3. Write the sequence:
- After calculating each step, we have the following sequence:
[tex]\[ 3, 10, 17, 24, 31, 38, 45, 52, 59, 66 \][/tex]
So, the first 10 numbers in the sequence, starting from 3 and adding 7 each time, are 3, 10, 17, 24, 31, 38, 45, 52, 59, and 66.
