The first term of an arithmetic progression (A.P.) is 7 and its common difference is 4. Wh… — JAMB UTME

The first term of an arithmetic progression (A.P.) is $7$ and its common difference is $4$ . What is the value of the $12^{\text{th}}$ term of the progression?

Answer: 51

Answer

The

12^{\text{th}}

term of the arithmetic progression is

51

Applying the arithmetic progression

n^{\text{th}}

term formula

T_n = a + (n - 1)d

with first term

a = 7

, common difference

d = 4

, and term index

n = 12

gives

T_{12} = 7 + (12 - 1) \times 4 = 7 + 44 = 51

Step-by-Step Solution

Identify given variables

a = 7

d = 4

, and

n = 12

These are the necessary components to calculate the required term position in an arithmetic sequence.

Apply the

n^{\text{th}}

term formula for an AP

T_{12} = 7 + (12 - 1) \times 4

The standard formula

T_n = a + (n - 1)d

determines the value of any term in an AP.

Compute the numerical result

T_{12} = 7 + 44 = 51

Multiplying the common difference by 11 and adding the first term yields the correct value.

Key Concept

Calculating the nth term of an Arithmetic Progression

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