Answer:
aₙ= n²-6
Step-by-step explanation:
The sequence:
- 5, -2, 3, 10, 19, ...
The difference between terms:
3, 5, 7, 9
The next term would be: 19+11= 30
Let's work out the formula:
- a₁= -5
- a₂= a₁+3= a₁+4-1= a₁+2²-1
- a₃= a₁+5= a₁+3+5= a₁+8= a₁+9-1= a₁+3²-1
- a₄= a₁+7= a₁+8+7= a₁+15= a₁+16-1= a₁+4²-1
- ...
- so
- we can put for nth term:
aₙ= a₁+n²-1= -5+ n²-1= n²-6
Let's test this formula for 5th and 6th terms:
- a₅= 5²-6= 25-6= 19
- a₆= 6² -6= 30
So the nth term is:
