The 5^{\text{th}} term of an arithmetic progression (AP) is 17 and its common difference i… — JAMB UTME

The $5^{\text{th}}$ term of an arithmetic progression (AP) is $17$ and its common difference is $3$ . What is the first term of the progression?

The first term of the progression is

5

The

n^{\text{th}}

term formula of an arithmetic progression is

T_n = a + (n - 1)d

. Substituting

T_5 = 17

n = 5

, and

d = 3

gives

17 = a + 4(3) = a + 12

. Isolating

a

yields

a = 17 - 12 = 5

Identify the given values and formula for the nth term of an AP.

The formula is

T_n = a + (n - 1)d

, with

T_5 = 17

n = 5

, and

d = 3

This formula connects the nth term, the first term, the number of terms, and the common difference.

Substitute the known values into the equation.

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

Subtracting 1 from the term index 5 gives 4, and multiplying by 3 gives 12.

Solve for the first term

a

a = 17 - 12 = 5

Subtracting 12 from both sides isolates

a

n-th term of an Arithmetic Progression

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