Answer:
a) aₙ=9n - 2
b) aₙ= (n+4)² -8, aₙ= (n+4)² -3, aₙ= (n+5)² -5
Step-by-step explanation:
a) 7, 16, 25, 34, 43, ...
AP with the first term of 7, and common difference of 9
aₙ= a₁+(n-1)d= 7+(n-1)*9= 7+9n-9= 9n -2
aₙ= 9n - 2
b) Pattern 1
If we assume
a₁= 3*2+3²
then
aₙ= 2(n+2) + (n+2)²= 2n+4+n²+4n+4= n²+8n+16- 8= (n+4)² -8
aₙ= (n+4)² -8
Pattern 2
If we assume
a₁=3*2 +(3+1)²
then
aₙ= 2(n+2)+(n+3)²= 2n+4+n²+6n+9= n²+8n+16 -3= (n+4)² - 3
aₙ= (n+4)² -3
Pattern 3
If we assume
a₁=3*2 +(3+2)²
then
aₙ= 2(n+2)+(n+4)²= 2n+4+n²+8n+16= n²+10n+25 -5= (n+5)² - 5
aₙ= (n+5)² -5
