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Home » Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
Arithmetic Progression | CBSE | Class 10 | Exercise 5.3 | Maths | NCERT Exemplar
Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Solution:

It is known to us that,

AP’s first term = a

The common difference = d.

According to the question given,

5th term, {{a}_{5}}~=\text{ }19

Using the nth term formula,

{{a}_{n}}~=\text{ }a+\left( n-1 \right)d

We obtain,

a\text{ }+\text{ }4d\text{ }=\text{ }19

a\text{ }=\text{ }19-4d…(1)

Also,

13th term – 8th term = 20

a\text{ }+\text{ }12d-\left( a\text{ }+\text{ }7d \right)\text{ }=\text{ }20

5d=20

d=4

Substituting the value of d = 4 in eq. 1,

We obtain,

a=\text{ }19-4\left( 4 \right)

a=3

As a result, the AP becomes,

3, 3 + 4 , 3 + 2(4),…

3, 7, 11,…

i

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