2.The Second Term Of An Arithmetic Sequence Is 24 And The Fifth Term Is 3.Find The First Term And The Common Differnce

2.the second term of an arithmetic sequence is 24 and the fifth term is 3.find the first term and the common differnce

 

ANSWER :

The common difference is -7 and the first term is 31.

STEP BY STEP EXPLANATION :

• Find the common difference by linear sistem.

A1 + 4R = 3 (-1)

A1 + 1R = 24

_______________

-A1 - 4R = -3

A1 + 1R = 24

_______________

-3R = 21

R = 21/(-3)

R = -7

• The first term.

An = A1 + (n - 1) × d

3 = A1 + (5 - 1) × (-7)

3 = A1 + 4 × (-7)

3 = A1 + (-28)

A1 - 28 = 3

A1 = 3 + 28

A1 = 31

Therefore , the common difference is -7 and the first term is 31.

OK.