Find the 320th term of 7, 10, 13, 16 … using Gauss’s strategy sequences
343
AAAaannndd the bot gets it wrong yet again!
No Gauss's strategy used here -- that was for determining the sum of a series.
a=7
d=3
a320 = 7 + 319*3 = 964
To find the 320th term of the sequence 7, 10, 13, 16, and so on, using Gauss's strategy, we need to determine the formula for the nth term of the sequence.
From the given sequence, we can observe that each term is obtained by adding 3 to the previous term:
7 + 3 = 10
10 + 3 = 13
13 + 3 = 16
So, the common difference between each term is 3. Therefore, we can use the formula for an arithmetic sequence to find the nth term.
The formula for the nth term of an arithmetic sequence is:
nth term (An) = a + (n - 1)d
Where:
- An is the nth term of the sequence
- a is the first term of the sequence
- d is the common difference between each term
- n is the position of the term in the sequence
In this case, the first term a is 7 and the common difference d is 3.
Using the formula, we can find the 320th term:
320th term (A320) = 7 + (320 - 1) * 3
= 7 + 319 * 3
= 7 + 957
= 964
Therefore, the 320th term of the sequence {7, 10, 13, 16, ...} is 964.
To find the 320th term of the given sequence, we can use Gauss's strategy of arithmetic sequences.
In an arithmetic sequence, each term is found by adding a constant difference to the previous term. In this sequence, the first term (a₁) is 7 and the common difference (d) is 3 (since each term is obtained by adding 3 to the previous term).
We can use the formula to find the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1) * d
where aₙ represents the nth term, a₁ is the first term, n is the position of the term we want to find, and d is the common difference.
To find the 320th term, we substitute a₁ = 7, d = 3, and n = 320 into the formula:
a₃₂₀ = 7 + (320 - 1) * 3
Simplifying the equation:
a₃₂₀ = 7 + 319 * 3
We can calculate this:
a₃₂₀ = 7 + 957
Therefore, the 320th term of the sequence is 964.
Using Gauss's strategy, we were able to find the 320th term by identifying the arithmetic nature of the sequence and applying the formula for arithmetic sequences.