The 5^{\text{th}} term of an arithmetic progression (AP) is 18 and its 11^{\text{th}} term… — JAMB UTME

The $5^{\text{th}}$ term of an arithmetic progression (AP) is $18$ and its $11^{\text{th}}$ term is $42$ . Calculate the value of the $20^{\text{th}}$ term of this progression.

Answer: 78

Answer

Using the AP general term formula

T_n = a + (n-1)d

, the equations

a + 4d = 18

and

a + 10d = 42

yield

d = 4

and

a = 2

. Evaluating

T_{20} = 2 + 19(4)

yields

78

Step-by-Step Solution

Set up simultaneous equations using the general term formula

T_n = a + (n-1)d

a + 4d = 18

and

a + 10d = 42

Relate given terms to the first term

a

and common difference

d

Solve for the common difference

d

6d = 24 \implies d = 4

Subtracting the 5th term equation from the 11th term equation eliminates

a

Solve for the first term

a

a + 16 = 18 \implies a = 2

Substitute the value of

d

back into the first equation.

Calculate the 20th term

T_{20} = 2 + 19(4) = 78

Apply the nth term formula for

n = 20

Key Concept

Determining terms of an Arithmetic Progression using simultaneous equations

Estimated Time:1m 30s

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