Answer :
The 9th term in the given arithmetic sequence is found using the common difference, which is 200. By applying the arithmetic sequence formula, the 9th term is calculated to be 1572.
Finding the 9th Term in the Sequence
To determine the 9th term in the sequence, let's first identify the pattern or common difference in the given sequence.
The sequence provided is:
-28, 172, 372, 572, 772,
We can observe that the sequence increases consistently. Let's find the common difference between the consecutive terms:
- 172 - (-28) = 200
- 372 - 172 = 200
- 572 - 372 = 200
- 772 - 572 = 200
The common difference, denoted as d, is 200.
To find the 9th term, we'll use the formula for the nth term of an arithmetic sequence:
an = a + (n - 1)d
Where a is the first term, d is the common difference, and n is the term number.
Given:
- a = -28
- d = 200
- n = 9
Substituting these values into the formula:
a9 = -28 + (9 - 1) × 200
= -28 + 8 × 200
= -28 + 1600
= 1572
So, the 9th term in the sequence is 1572.
Answer:
1572 is the answer.
Step-by-step explanation:
-28,172,372,572,772
divide by 4:-
-7,43,93,143,193
Here common difference is +50.
So,
using the formula:-
nth term = {a+d(n-1)} * 4
= {-7 + 50(n-1) } * 4
= {-7 + 50n - 50} * 4
= 200n - 228
Now,
9th term = 200(9) - 228 = 1572.
