Because the difference between any term and the previous term is a constant, this is an arithmetic sequence because of that constant which is referred to as the common difference, d. Which in this case is -35--38=-32--35=3
Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.
In this case a=-38 and d=3 so
a(n)=-38+3(n-1) which we can simplify to
a(n)=-38+3n-3
a(n)=3n-41, so the 52nd term is:
a(52)=3(52)-41
a(52)=156-41
a(52)=115
Answer is 3a²b (a + b)
Step-by-step explanation:
- Step 1: Find 3a² (ab²+b²)
⇒ 3a² (ab²+b²) = 3a³b + 3a²b² = 3a²b (a + b)
