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4 years ago

The 6th term of an Arithmetic Progression is 17 and the 13th term is 38. Determine the 19th term

Mathematics

1 answer:

Sonja [21]4 years ago

4 0

Answer:

Step-by-step explanation:

The n th term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₆ = 17 and a₁₃ = 38, then

a₁ + 5d = 17 → (1)

a₁ + 12d = 38 → (2)

Subtract (1) from (2) term by term to eliminate a₁

7d = 21 ( divide both sides by 7 )

d = 3

Substitute d = 3 into (1) and evaluate for a₁

a₁ + 5(3) = 17

a₁ + 15 = 17 ( subtract 15 from both sides )

a₁ = 2

Thus

$a_{19}$ = 2 + (18 × 3) = 2 + 54 = 56

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Step-by-step explanation:

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4 years ago

The 6th term of an Arithmetic Progression is 17 and the 13th term is 38. Determine the 19th term ​

The 6th term of an Arithmetic Progression is 17 and the 13th term is 38. Determine the 19th term