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Find the indicated term of the arithmetic sequence : 1. a16 = 96 and a43 = 231, find a116. 2. a1...

Question:

Find the indicated term of the arithmetic sequence :

1. a16 = 96 and a43 = 231, find a116.

2. a1 = 4 and a4 = 108, find a10.

Arithmetic Sequence-Terms and Properties:

A sequence in the form of, {eq}a,a+d,a+2d,a+3d,...................., {/eq} is called an arithmetic sequence where a is the first term and d is the common difference of the sequence.

Here it is clear that the difference between any two continuous terms is constant.

The nth term of an arithmetic sequence is measured by a simple formula that is as follows-

$$a_{n} = a+(n-1)d $$

here {eq}a_{n} {/eq} is the nth term

An arithmetic sequence can have a finite or infinite number of terms.

The sum of first n terms of an arithmetic sequence is calculated as-

$$S_{n} = \frac{n}{2}[2a+(n-1)d] $$

here {eq}S_{n} {/eq} is the sum of {eq}n {/eq} terms

Answer and Explanation: 1

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(1)

Given terms of an arithmetic sequence are-

$$\begin{align} a_{16} &= 96 \\[0.3cm] a+(16-1)d &= 96 \\[0.3cm] a+15 d &= 96 \tag{Eq.1}...

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How and Why to Use the General Term of an Arithmetic Sequence

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Chapter 21 / Lesson 5
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Learn the definition of arithmetic sequence and general term of a sequence. Learn the formula for general term of a sequence and see examples.


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