Question

the sum of the first n terms of an ap is given by n(n+3). find the 19th term of the ap​

Answer 1

Answer:

The 19th term of the AP is 40.

Step-by-step explanation:

Given that,

The sum of the first n terms of an AP is = n(n + 3)

ie, Sₙ = n(n + 3)

S₁ = a₁ = 1(1 + 3)

S₁ = 1(4)

S₁ = a1 = 4

S₂ = 2(2 + 3)

S₂ = 2(5)

S₂ = 10

∴ a₂ = S₂ - S₁

∴ a₂ = 10 - 4

a₂ = 6

d = a₂ - a₁

d = 6 - 4

d = 2

To find,

The 19th term of an AP.

∴ n = 19

By using general term formula,

aₙ = a + (n - 1)d

a₁₉ = 4 + (19 - 1)2

a₁₉ = 4 + 36

$\large{\bold{\mathsf{\pink{a_{19} = 40}}}}$

Therefore, the 19th term of the AP is 40.

Answer 2

Answer:

Step-by-step explanation:

The sum of the first n terms of an AP is = n(n + 3)

ie, Sₙ = n(n + 3)

S₁ = a₁ = 1(1 + 3)

S₁ = 1(4)

S₁ = a1 = 4

S₂ = 2(2 + 3)

S₂ = 2(5)

S₂ = 10

∴ a₂ = S₂ - S₁

∴ a₂ = 10 - 4

a₂ = 6

d = a₂ - a₁

d = 6 - 4

d = 2

To find,

The 19th term of an AP.

∴ n = 19

By using general term formula,

aₙ = a + (n - 1)d

a₁₉ = 4 + (19 - 1)2

a₁₉ = 4 + 36

Therefore, the 19th term of the AP is 40.