Write the algebra of 17,20,23,26..Is 400 a term of this sequence
To find the algebraic expression for the given sequence, we can notice that each term increases by 3. Therefore, we can start with the first term, 17, and add 3 repeatedly to find the subsequent terms.
Let's denote the first term as 'a' and the common difference between subsequent terms as 'd'. In this case, a = 17 and d = 3.
The algebraic expression for the sequence is given as:
Term(n) = a + (n - 1) * d
Now, we can substitute the values of 'a' and 'd' in the expression:
Term(n) = 17 + (n - 1) * 3
To find out if 400 is a term in this sequence, we can set up an equation and solve for 'n':
17 + (n - 1) * 3 = 400
Simplifying the equation:
(n - 1) * 3 = 400 - 17
(n - 1) * 3 = 383
Dividing both sides of the equation by 3:
n - 1 = 383/3
n - 1 ≈ 127.67
Adding 1 to both sides of the equation:
n ≈ 128.67
Since 'n' represents a term in the sequence, it must be a whole number. Therefore, 400 is not a term in this sequence.
looks like an arithmetic sequence with a = 17 and d = 3
term(n) = a + (n-1)d
400 = 17 + (n-1)(3)
383 = 3n - 3
3n =386
n = 386/3 , which is not a whole number, so NO, 400 is not part of the sequence