Q. 14.0( 21 Votes )

# Fill in the blanks in the following table, given that a is the first term, d the common difference and the nth term of the AP:

Answer :

I. Given first term (a) = 7

Common difference (d) = 3

n = 8 ,

a_{n} = ?

we know that a_{n} = a + (n-1)d

So, we have to find a_{8}

a_{8} = a + (8-1)d = 7 + 7 × 3 = 28

II.

Given first term (a) = -18

Common difference (d) = ?

n = 10, a_{n} = 0

a_{10} = a + (10-1)d

0 = -18 + 9×d

d = 2

III. Given

Common difference (d) = -3

n = 18, a_{n} = -5

first term (a) = ?

a_{8} = a + (18-1)d

-5 = a + 17×(-3)

a = -46

IV. Given first term (a) = -18.9

Common difference (d) = 2.5

n = ?

a_{n} = 3.6

we know that a_{n} = a + (n-1)d

3.6 = -18.9 + (n-1)2.5

22.5 = (n-1)2.5

9 = n-1

n = 10

V. Given first term (a) = 3.5

Common difference (d) = 0

n = 105 ,

a_{n} = ?

we know that a_{n} = a + (n-1)d

a_{n} = 3.5 + (105-1)0

a_{n} = 3.5

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