Question

5,7,12,21,35,55,? find answer

Answer 1

Answer:

First, let’s assume that 5 is the 0th term, 11 is the 1st term, and so on. Now, find the difference between the terms.

11−5=6

21−11=10

35−21=14

53−35=18

We can see that the amount added to each term is increasing by four each time, starting at 6. This is an arithmetic sequence, a detail that will be important later on.

Additionally, we can rewrite each term as follows:

5=5

11=5+6

21=5+6+10

35=5+6+10+14

53=5+6+10+14+18

We can see a pattern emerging: each term is 5 plus the sum of the arithmetic sequence above. Since the sum of an arithmetic sequence is n(2a+(n−1)d)2 , where a is the first term and d is the amount increasing each time, we can write:

tn=5+n(2×6+(n−1)×4)2

This can be simplified into:

tn=2n2+4n+5

Explanation:

mark breainest