Question

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

Answer 1

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,

13^th term – 8^th term = 20

a + 12d – (a + 7d) = 20

5d = 20

d = 4

Substituting d = 4 in equation 1,

We get,

a = 19 – 4(4)

a = 3

Then, the AP becomes,

3, 3 + 4, 3 + 2(4),...

3, 7, 11,...