# Arithmetic Progressions

#### Question 3:

In the following APs find the missing term in the boxes

**I.**

**II.**

**III.**

**IV.**

**V.**

#### Answer:

**I.**

For this A.P.,

*a*
= 2

*a*_{3}
= 26

We
know that, *a*_{n} = *a* + (*n* −
1) *d*

*a*_{3}
= 2 + (3 − 1) *d*

26
= 2 + 2*d*

24
= 2*d*

*d*
= 12

*a*_{2}
= 2 + (2 − 1) 12

= 14

Therefore, 14 is the missing term.

**II.**

For this A.P.,

*a*_{2}
= 13 and

*a*_{4}
= 3

We
know that, *a*_{n} = *a* + (*n* −
1) *d*

*a*_{2}
= *a* + (2 − 1) *d*

13
= *a* + *d* (I)

*a*_{4}
= *a* + (4 − 1)* d*

3 =
*a* + 3*d* (II)

On subtracting (I) from (II), we obtain

−10
= 2*d*

*d*
= −5

From equation (I), we obtain

13
= *a* + (−5)

*a*
= 18

*a*_{3}
= 18 + (3 − 1) (−5)

= 18 + ...

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