Question

If a2 = 4 and a5 = 13 then find a10​

Answer 1

Step-by-step explanation:

A2 = a+ d

4 = a+d----------1

A5 = a+ 4d

13 = a+d+3d ------2

from 1, a+d=4

13 = 4+3d

9 = 3d

d = 3

putting value of d in 1

4 = a+ 3

a = 1

A10 = a+9d

= 1+ 9(3)

= 1+ 27

=28

Answer 2

Answer:

The tenth term ( a₁₀ ) of the AP is 28.

Step-by-step-explanation:

We have given that,

For an AP,

• a₂ = 4
• a₅ = 13

We have to find a₁₀ of the AP.

Now, we know that,

aₙ = a + ( n - 1 ) * d - - - [ Formula ]

⇒ a₂ = a + ( 2 - 1 ) * d

⇒ 4 = a + d

⇒ a = 4 - d - - - ( 1 )

Now,

a₅ = a + ( 5 - 1 ) * d

⇒ 13 = a + 4d

⇒ 13 = ( 4 - d ) + 4d - - - [ From ( 1 ) ]

⇒ 4 - d + 4d = 13

⇒ 4 + 3d = 13

⇒ 3d = 13 - 4

⇒ 3d = 9

⇒ d = 9 ÷ 3

⇒ d = 3

Now,

a₁₀ = a + 9d

⇒ a₁₀ = ( 4 - d ) + 9d - - - [ From ( 1 ) ]

⇒ a₁₀ = 4 - d + 9d

⇒ a₁₀ = 4 + 8d

⇒ a₁₀ = 4 + 8 * 3

⇒ a₁₀ = 4 + 24

⇒ a₁₀ = 28

∴ The tenth term ( a₁₀ ) of the AP is 28.