The Second Term Of Arithmetic Sequence Is 24 And The Fifth Term Is 3.Find The First Term And The Common Difference ...Please Show Me Your Solution

The second term of arithmetic sequence is 24 and the fifth term is 3.Find the first term and the common difference ...please show me your solution

 

Answer:

First term (a₁) = 31

Common difference (d) = -7

Step-by-step explanation:

Arithmetic sequence general nth rule:

an = a₁ + (n-1)(d)

Where:

an = last term

n = the number of terms in a sequence or the nth term

a₁ = first term

d = common difference

Given:

a₂ = 24;  n=2

24 = a₁ + (2-1)(d)

24 = a₁ + d

a₁ = 24-d  

a₅ = 3; n = 5

3 = a₁ + (5-1)(d)  

a1 = 3 - 4d

Find d, the common difference by equating 24-d and 3-4d:

24 - d = 3 - 4d

4d - d = 3 - 24

3d/d = -21/3

d = -7

Find the first term, a₁:

a₁ = 3-4d

a₁ = 3 - 4(-7)

a₁ = 3 + 28

a₁ = 31

OR

a₁ = 24 - d

a₁ = 24 - (-7)

a₁ = 24 +7

a₁ = 31


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