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Arithmetic Progressions

Question 1:

Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.

a

d

n

an

I

7

3

8

…...

II

− 18

…..

10

0

III

…..

− 3

18

− 5

IV

− 18.9

2.5

…..

3.6

V

3.5

0

105

…..

Answer:

I. a = 7, d = 3, n = 8, an = ?

We know that,

For an A.P. an = a + (n − 1) d

= 7 + (8 − 1) 3

= 7 + (7) 3

= 7 + 21 = 28

Hence, an = 28

II. Given that

a = −18, n = 10, an = 0, d = ?

We know that,

an = a + (n − 1) d

0 = − 18 + (10 − 1) d

18 = 9d

Hence, common di…

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