Question

which term of the series:
21, 18, 15, .............is -81 ?
can any term of this series be zero ? if yes, find the number of terms.....


guys plsss answer it fast.....

its urgent ​

Answer 1

Given :-

AP = 21, 18, 15 .... -81

Here,

First term = a = 21

Common difference = d = 18 - 21 = -3

An = -81

General form of AP :-

a + (n - 1)d = An

Therefore 21 + (n - 1)(-3) = -81

➡ 21 + (-3n + 3) = -81

➡ 21 - 3n + 3 = -81

➡ 24 - 3n = -81

➡ -3n = -81 - 24

➡ -3n = -105

➡ n = -105/-3

➡ n = 35

Hence, the 35th term of the given AP is -81.

Now, we've to find out if 0 is any term of the given AP.

Let us take An as 0 and consider that 0 is any term of the given AP.

➡ a + (n - 1)d = 0

➡ 21 - 3n + 3 = 0

➡ 24 - 3n = 0

➡ -3n = -24

➡ n = -24/-3

➡ n = 8

Hence, 0 is a term of the given AP.

Answer 2

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

${\mathfrak{\underline{\underline{Step-By-Step-Explanation:-}}}}$

✯ A.P = 21,18,15.............-81

So, a (first term) = 21

d (difference) = 18 - 21 = -3 ________________________________

So, we have :-

✯ Case 1

an = -81

We have formula :-

$\huge{\sf{\boxed{\boxed{A_{n} \: = \: a \: + \: (n-1)d}}}}$

_______________[Put values]

⟹ -81 = 21 + (n-1)(-3)

⟹ -81 - 21 = -3n + 3

⟹ -102 = -3n + 3

⟹ -102 -3 = -3n

⟹ -105 = -3n

⟹ 105 = 3n

⟹ n = 105/3

⟹ n = 35

✯ So, -81 is on 35th term of AP

$\huge{\sf{\boxed{\boxed{n \: = \: 35}}}}$

____________________________

✯ Case 2

Yes , the AP have a term as zero

_____________________________

Put an = 0

So, Use the same formula

$\huge{\sf{\boxed{\boxed{A_{n} \: = \: a \: + \: (n-1)d}}}}$

___________[Put values]

0 = 21 + (n-1)(-3)

⟹ 0 = 21 - 3n + 3

⟹ 0 = 24 - 3n

⟹ -24 = -3n

⟹ 3n = 24

⟹ n = 24/3

⟹ n = 8

$\huge{\sf{\boxed{\boxed{n \: = \: 8}}}}$