An arithmetic progression (A.P.) has a fifth term of 17 and a common difference of 3. What… — JAMB UTME

An arithmetic progression (A.P.) has a fifth term of $17$ and a common difference of $3$ . What is the first term of the progression?

The first term of the progression is

5

Using the

n^{\text{th}}

term formula for an arithmetic progression,

T_n = a + (n - 1)d

, substituting

T_5 = 17

n = 5

, and

d = 3

gives

17 = a + 4(3) \implies 17 = a + 12 \implies a = 5

Identify the given parameters and formula for the

n^{\text{th}}

term of an A.P.

Formula:

T_n = a + (n - 1)d

, where

T_5 = 17

n = 5

, and

d = 3

The standard formula connects the

n^{\text{th}}

term, first term, term position, and common difference.

Substitute the given values into the formula.

17 = a + (5 - 1) \times 3 \implies 17 = a + 4 \times 3 \implies 17 = a + 12

Evaluating

(n - 1)d

gives the total difference added to the first term.

Solve for the first term

a

a = 17 - 12 = 5

Subtracting

12

from both sides isolates

a

Arithmetic Progression

n^{\text{th}}

term calculation

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