Question

Write the algebraic form of the arithmetic sequence 4 7 10

Answer 1

Answer:

X=4

X+3=7

7=Y

X+Y=10

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Step-by-step explanation:

Answer 2

The required algebraic form of the sequence is 1+3n.

Given:

The arithmetic sequence: 4, 7, 10, ...

To Find:

The algebraic form of the given arithmetic sequence.

Solution:

A sequence is said to be in arithmetic progression (AP) if the difference between every two consecutive numbers in the sequence is the same.

The $n^{th}$ term of a sequence in AP is given by $a_{n}$ = a+(n-1)d, where 'a' is the first term, n'' is the number of terms in the sequence, and 'd' is the common difference.

We are given a sequence 4, 7, 10, ...

This sequence is in AP as the difference between every two consecutive numbers is 3.

So, the first term a = 4

The common difference d = 3.

The general form that represents the given sequence will be,

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

⇒ $a_{n}$ = 4+(n-1)3

⇒ $a_{n}$ = 1 + 3n.

Hence, the required algebraic form of the sequence is 1+3n.

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