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Find out when the numbers in the sequence 121, 117, 113 first start going down. We’ll guide you step by step to understand how the pattern changes.
Which term of the A.P. 121, 117, 113 … is its first negative term?
The 32nd term is teh first negative term in the sequence A.P. 121, 117, 113..
Here’s how:
The given sequence is an arithmetic progression with first term 121 and common difference -4. We want to find the term where the sequence first becomes negative.
Let the nth term be negative. Then, the nth term is given by:
a_n = a + (n – 1)d = 121 + (n – 1)(-4) < 0
Solving for n, we get:
n – 1 > 121 / 4 n > 31.25
Since n must be a positive integer, the smallest possible value of n is 32. Therefore, the 32nd term is the first negative term in the sequence.
What is Arithmetic Progression?
An arithmetic progression (AP) is a sequence of numbers where the difference between every two consecutive terms is the same. This constant difference is called the common difference. For example, the sequence 2, 5, 8, 11, 14, … is an arithmetic progression with a common difference of 3.
Here are some key properties of arithmetic progressions:
- The first term of an AP is denoted by a.
- The nth term of an AP is given by the formula: a_n = a + (n – 1)d, where d is the common difference.
- The sum of the first n terms of an AP is given by the formula: Sn = n/2 (2a + (n – 1)d).
Arithmetic progressions have many applications in mathematics, physics, and other fields. For example, they can be used to model the motion of an object under constant acceleration, or to calculate the sum of a series of numbers.
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