1, a.) The two specific conjectures are in the first image.
1, b.) The two general conjectures are in the second image.
2, a.) Two specific conjectures for this pattern are:
- The common difference between two consecutive terms is 3.
- And the given difference is A.P.
2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.
For finding its nth term we can use the formula: a(n) = a + (n-1) x d.
2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.
Answer:
Bottom prism: 126*11=1386
Top Prism: 2*45=90
Total volume: 1386+90= 1746 cubic cm
I assume you're asking to solve for the n-th term in the sequence,
.
From the given recursive rule,

and by substitution,

Similarly,


The pattern continues, so that we can write the n-th term in terms of the 1st one:

So the first few terms of the sequence are
{10, 12, 14, 16, 18, 20, …}
Answer:
4
Step-by-step explanation:
set it up as a fraction, 3/25, x/38. cross multiply, 3*38 then divide by 25 which is 4.56