Question

Q. The first term of an arithmetic sequence is 8 and common difference is 5.

a. Write first three terms of the sequence.

b. Find the algebraic form of the sequence.​

Answer 1

Answer:

a. The first three terms are 8, 13, 18

b. The algebraic form of the sequence is 5n + 3

Step-by-step explanation:

a. It's given that the first term is 8 and the common difference between the terms is 5. So, simply add 5 in each term.

                  8, (8+5), (8+5+5),.... = 8, 13, 18,....

b. Arithmetic sequence formula = a + (n-1) d   (where a is the first term, n is the number of terms and d is the common difference)

 

                                Arithmetic sequence =  8 + (n - 1) (5)

                                                                    =  8 + 5n - 5

                                                                    =  5n + 3

Answer 2

Answer:-

$\blue{\bigstar}$ First three terms of the sequence are $\large\leadsto\boxed{\rm\pink{8 , 13 \: and \: 18}}$

$\blue{\bigstar}$ The algebraic form of the sequence is $\large\leadsto\boxed{\rm\pink{A_n = 5n + 3}}$

• Given:-

• First term of an A.P is 8

• Common difference is 5

• To Find:-

• First three terms of the sequence

• Algebraic form of the sequence

• Solution:-

Given that,

• First term(a) = 8

• Common difference (d) = 5

a.)

The first three terms of an A.P will be a, a+d and a+2d .

Hence,

• a = 8

• a+d = 8 + 5 = 13

• a+2d = 8 + 2(5) = 8 + 10 = 18

Therefore, the 1st three terms are 8 , 13 and 18.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀

b.)

The algebraic form of the sequence will be given by

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\purple{A_n = a + (n-1) d}}}$

➪ $\sf A_n = 8 + (n-1) 5$

➪ $\sf A_n = 8 + 5n - 5$

★ $\bf\red{A_n = 5n + 3}$

Therefore, the algebraic form of the given A.P will be 5n + 3.