Question

First term of an arithmetic sequence is 5 and the common difference is 3. Write the algebraic expression of the sequence.​

Answer 1

Step-by-step explanation:

first term is 5 common difference is 3

so the sequence is

5,8,11,14,17,20

Answer 2

Answer:

Required algebraic expression is $a_n = 3n - 2$Where n is the number of term.

Step-by-step explanation:

Given informations :

This is an Arithmetic progression. First term of the sequence is 5 and common difference of the terms is 3.

Here we want to find Algebraic expression of this Sequence.

In Arithmetic progression,we denote nth term by $a_n$

We know,

$a_n = a + (n - 1)d......(1)$

Where a is the first term if the series and n is number of terms and d is common difference.

According to question,

$a = 5 \\ d = 3$

From equation (1),

$a_n = 5 + (n - 1) \times 3$

$a_n = 5 + 3n - 3$

$a_n = 3n - 2$

This is algebraic expression of the sequence, where n is the number of term.

For example of we put n=5 then we can find

$a_5 = 3 \times 5 - 2 = 13$

Therefore 13 is the 5th term of this sequence.

Some other important formulas of Arithmetic progression,

1.General from of Ap series-$a,a+d,a+2d,a+3d,.........a+nd$

2.Sum of nth term of AP series$= \frac{n}{2} [2a + (n - 1)d$

3.Sum of all terms in a finite AP with the last term as "l"=$\frac{n}{2} (a + l)$