find the formulas of the Next three terms rule of 36, 49, 64, 81, .....
next three terms are 100,121,144
here the formula is 6^2,(6+1)^2,(6+2)^2,.............
The difference in each term is:
13, 15, 17
So each time, the difference is increased by 2
The genera; formula for the next 3 terms:
(T_n-1 - T_n-2 + 2) + T_n-1 = T_n
=>
2*(T_n-1) -(T_n-2) + 2 = T_n
let n = the number of term (1,2,3..ect)
For the 5th term, apply the general formula:
n=5
2*T_4 - T_3 + 2 = T_5
2*81 - 64 + 2 = T_5
try for the next 2 terms.
Grow eh5yjthnbgfrgh
To find the formulas of the next three terms in the given sequence 36, 49, 64, 81, ..., we need to first identify the pattern or rule governing the sequence. Let's examine the differences between consecutive terms:
- The difference between 49 and 36 is 13.
- The difference between 64 and 49 is 15.
- The difference between 81 and 64 is 17.
From this observation, we can conclude that the differences between the terms are increasing by 2 each time.
To find the rule for the sequence, we can consider the sequence of differences: 13, 15, 17, ...
Looking at the differences, we can see that they are consecutive odd numbers (starting from 13).
Therefore, the rule for the differences is that each term is obtained by adding 2 to the previous term.
Now, let's find the formulas for the next three terms in the original sequence:
To find the 5th term:
- The 4th term is 81, so we add the last difference of 17: 81 + 17 = 98
To find the 6th term:
- The 5th term is 98, so we add the next difference of 19: 98 + 19 = 117
To find the 7th term:
- The 6th term is 117, so we add the next difference of 21: 117 + 21 = 138
Therefore, the formulas for the next three terms in the sequence are: 98, 117, and 138.