Question

The first term of an arithmetic sequence is 3 and common difference 4
a.write the algebraic expression of this sequence?
b.what is its 10th term?

Answer 1

Answer:

first tirm a=3

and d =4

then expression is = a,a+d,a+2d,a+3d

=3,3+4,3+2×4,3+3×4

=3,7,11,15

b) 10th term is = a+9d= 3+9×4=39

Answer 2

Answer:

a) The algebraic expression for the given sequence is $a_{n} =4n-1$

b) $10th$ term $ax_{10} =39$ .

Step-by-step explanation:

Arithmetic Progression is a sequence of numbers which either increases or decreases by a fixed number. This fixed number is called the common difference, denoted by d , it can be positive, negative or zero.

First term of an AP is denoted by a , and the general term as $a_{n}$ .

We have the formula for $a_{n}$ as  $a_{n} =a+(n-1)d$ .

Here $a=3$ and $d=4$ .

a) The algebraic expression for this sequence refers to the general term of the sequence

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

     $=3+(n-1)4\\\\=3+4n-4\\\\=4n-1$.

b) The term  $a_{10} =a+(10-1)d$

                           $=3+9*4\\\\=3+36\\\\=39$ .

Hence the answer.

thank you