Question

Find the 15th term the sequence if a8=5 and a21=-60

Answer 1

Answer

• The 5th term of the AP is -30

Explanation

Given

• a₈ = 5
• a₂₁ = -60

To Find

• The 15thbterm of the AP?

Solution

Using the formula aₙ = a+(n-1)d

• a₈ = a+7d = 5 -eq(1)
• a₂₁ = a+20d = -60 -eq(2)

Subtracting these two Equations

a+20d = -60

a+7d = 5

━━━━━━━━

13d = -65

━━━━━━━━

→ d = -65/13

→ d = -5

Substituting this in the first Equation

→ a+7(-5) = 5

→ a-35 = 5

→ a = 5+35

→ a = 40

✭ 15th term of the AP

→ aₙ = a+(n-1)d

→ a₁₅ = 40+(15-1)(-5)

→ a₁₅ = 40+(14)(-5)

→ a₁₅ = 40+(-70)

→ a₁₅ = -30

Answer 2

✧Answer :

• The 5th term of the AP is -30

✧Given:

• a₈ = 5
• a₂₁ = -60

✧To Find:

• The 15thbterm of the AP?

✧Solution :

★★Formula used :

• aₙ = a+(n-1)d

Here equations formed :-

• a₈ = a+7d = 5 -eq(1)
• a₂₁ = a+20d = -60 -eq(2)

Subtracting these two Equations

→a+20d = -60

→a+7d = 5

_____________________________________

→13d = -65

_____________________________________

→ d = -65/13

→ d = -5

Substituting this in the first Equation:

→ a+7(-5) = 5

→ a-35 = 5

→ a = 5+35

→ a = 40

✭ 15th term of the AP

→ aₙ = a+(n-1)d

→ a₁₅ = 40+(15-1)(-5)

→ a₁₅ = 40+(14)(-5)

→ a₁₅ = 40+(-70)

→ a₁₅ = -30

$\rule{300}{2}$