Question

If 6th term in ap is 10 ,10th term is _26 find 15th term?

Answer 1

Answer:

fifteenth term of AP is 46.

Step-by-step explanation:

Given :

• 6th term of AP = 10
• => a + 5d = 10.......(1)

• 10th term of AP = 26
• => a + 9d = 26.......(2)

To find :

• Fifteenth term of AP

Solution :

Solving eq (1) and (2),

a + 9d = 26

a + 5d = 10

-⠀-⠀⠀⠀-

___________

4d = 16

=> d = 16/4

=> d = 4

_____________

Now, put the value of d in (1),

=> a + 5(4) = 10

=> a + 20 = 10

=> a = -10

Fifteenth term = a + 14d

=> Fifteenth term = -10 + 14(4)

=> Fifteenth term = -10 + 56

=> Fifteenth term = 46

Therefore, fifteenth term of AP is 46.

Answer 2

Answer:

★ 15th term will be 46 ★

Step-by-step explanation:

Given:

• 6th term of AP is 10
• 10th term of AP is –26

To Find:

• 15th term of AP

→Term of an AP : An = a + ( n – 1) d

Solution: Let a is first term and d is common difference

→For sixth term

$\small\implies{\sf }$ a6 = a + ( 6 – 1 ) d

$\small\implies{\sf }$ a6 = a + 5d

$\small\implies{\sf }$ 10 = a + 5d..............(1)

→For tenth term

$\small\implies{\sf }$ a10 = a + ( 10 – 1 ) d

$\small\implies{\sf }$ a10 = a + 9d

$\small\implies{\sf }$ 26 = a + 9d..............(2)

★ Now Subtracting equation (1) from equation (2) ★

26 = a + 9d

10 = a + 5d

(-) ⠀(-) ⠀ (-)

_________________

⠀16 = 4d

$\small\implies{\sf }$ 16 = 4d

$\small\implies{\sf }$ d = 16 / 4 = 4

★Substitute the value of d = 4 in equation 1 ★

→ 10 = a + 5d

→ 10 = a + 5 x 4

→ 10 = a + 20

→ 10 – 20 = a

→ –10 = a

★ Now, Finding the 15th term ★

$\small\implies{\sf }$ a15 = a + (n-1)d

$\small\implies{\sf }$ a15 = (–10) + (15–1) 4

$\small\implies{\sf }$ a15 = –10 + 14 x 4

$\small\implies{\sf }$ a15 = 46

Hence, 15th term is 46