Question

third term of an Ap is 12 and seventh term of an Ap is 24 then find 10th term​

Answer 1

Answer:

3rd term of AP = 12

⇒ a + (n-1)d = 12

a + (3-1)d = 12

a + 2d = 12

a = 12 - 2d — (i)

7th term of AP = 24

⇒ a + (n-1)d = 24

a + (7-1)d = 24

a + 6d = 24

a = 24 - 6d — (ii)

Now we compare both the equations:-

Since we know that both the equations stand for the value of ‘a’, we can say that they are equal to each other.

12 - 2d = 24 - 6d

6d - 2d = 24 - 12

4d = 12

d = 3

Now we find the value of ‘a’ by substituting the value of ‘d’ in equation (i):-

a = 12 - 2d

a = 12 - 2(3)

a = 12 - 6

a = 6

Now we find the value of the 10th term of AP:-

Formula = a + (n-1)d

6 + (10-1)3

6 + (9)3

6 + 27

33 Ans

10th term of AP = 33

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Answer 2

Answer:

The 10th term of the AP is 33.

Step-by-step-explanation:

For an AP,

• t₃ = 12
• t₇ = 24

We have to find the 10th term of AP.

We know that,

tₙ = a + ( n - 1 ) * d

⇒ t₃ = a + ( 3 - 1 ) * d

⇒ 12 = a + 2d

⇒ a = 12 - 2d - - - ( 1 )

Also,

t₇ = a + ( 7 - 1 ) * d

⇒ 24 = a + 6d

⇒ a + 6d = 24

⇒ ( 12 - 2d ) + 6d = 24 - - - [ From ( 1 ) ]

⇒ 12 - 2d + 6d = 24

⇒ 12 + 4d = 24

⇒ 4 ( 3 + d ) = 24

⇒ d + 3 = 24 / 4

⇒ d + 3 = 6

⇒ d = 6 - 3

⇒ d = 3

By substituting d = 3 in equation ( 1 ),

a = 12 - 2d - - - ( 1 )

⇒ a = 12 - 2 * 3

⇒ a = 12 - 6

⇒ a = 6

Now,

t₁₀ = a + ( 10 - 1 ) * d

⇒ t₁₀ = 6 + 9 * 3

⇒ t₁₀ = 6 + 27

⇒ t₁₀ = 33

∴ The 10th term of the AP is 33.