Determine the AP whose fifth term is 19 and the difference of the eigh

1.	Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Answer» We know that, The first term of an AP = a And, the common difference = d. According to the question, 5^th term, a₅ = 19 Using the n^th term formula, a_n = a + (n – 1)d We get, a + 4d = 19 a = 19 – 4d …(1) Also, 20^th term – 8^th term = 20 a + 19d – (a + 7d) = 20 12d = 20 d = 4/3 Substituting d = 4/3 in equation 1, We get, a = 19 – 4(4/3) a = 41/3 Then, the AP becomes, 41/3, 41/3 + 4/3 , 41/3 + 2(4/3) 41/3, 15, 49/3

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Answer»

We know that,

The first term of an AP = a

And, the common difference = d.

According to the question,

5^th term, a₅ = 19

Using the n^th term formula,

a_n = a + (n – 1)d

We get,

a + 4d = 19

a = 19 – 4d …(1)

Also,

20^th term – 8^th term = 20

a + 19d – (a + 7d) = 20

12d = 20

d = 4/3

Substituting d = 4/3 in equation 1,

We get,

a = 19 – 4(4/3)

a = 41/3

Then, the AP becomes,

41/3, 41/3 + 4/3 , 41/3 + 2(4/3)

41/3, 15, 49/3