The fourth term of an arithmetic progression (A.P.) is 15 and the ninth term is 35. What i… — JAMB UTME

The fourth term of an arithmetic progression (A.P.) is $15$ and the ninth term is $35$ . What is the common difference of the progression?

Answer: 4

The common difference of the arithmetic progression is

4

Using the A.P. term formula

T_n = a + (n-1)d

, the fourth term gives

a + 3d = 15

and the ninth term gives

a + 8d = 35

. Subtracting the two equations yields

5d = 20

, which simplifies directly to

d = 4

Express the given terms using the n-th term formula

T_n = a + (n-1)d

a + 3d = 15

and

a + 8d = 35

The

n^{\text{th}}

term formula relates any term to the first term (

a

) and common difference (

d

Subtract the equation for the fourth term from the ninth term

5d = 20

Subtracting eliminates the first term

a

and leaves a simple equation in terms of

d

Divide by

5

to solve for

d

d = 4

Dividing both sides of

5d = 20

5

gives the common difference.

Finding the common difference of an Arithmetic Progression given two non-consecutive terms

Question