Question

3. Find the 15th term of the sequence if a8= 5 and a21 = -60​

Answer 1

Step-by-step explanation:

-60-5/21-8

-65/13

-5

there fore common difference is -5

15th term = 8th term + 7d

= 5+ 7× -5

= -30

Answer 2

15th term of the sequence is - 30

Given:  

8th term of the sequence, a₈ = 5

21th term of the sequence, a₂₁ = - 60

To find:

15th term of the sequence  

Solution:

We know that nth term of the sequence a$_{n}$= a+(n-1)d  

Then a₈ = a +(8-1)d = 5

⇒ a + 7d = 5 _(1)

a₂₁ = a + (21-1) d = - 60

⇒ a +20d = - 60 _(2)

Subtract (1) from (2)

⇒ a +20d - ( a + 7d) = - 60 - 5

⇒ a + 20d - a - 7d = - 65

⇒ 13 d = - 65

⇒ d = - 5

Now substitute d = - 5 in (1)

⇒ a + 7(-5) = 5

⇒ a - 35 = 5

⇒ a = 40

15th term of sequence a₁₅ = 40 + (15 - 1) -5

⇒  a₁₅ = 40 + (14)- 5

⇒  a₁₅ = 40 - 70 = - 30

15th term of the sequence is - 30

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