Question

Which term of AP 21 , 18, 15, ............. is -81 ?also is an term 0 Give reason for your answer ??????

Answer 1

heya.....

your answer
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a1 = 21 , d = -3 , an = -81

here, a1 is first term
d is common difference
an is nth term
n =?

we know,

An = a1 + (n-1) d
-81 = 21 + (n-1) (-3)
-81 -21 /-3 = n-1
-102/-3 = n-1
34 +1 = n
n = 35

so, 35th term is -81

(ii) a1 = 21 , d= -3, An = 0, n = ?

An = a1 + (n-1) d
0 = 21 + (n-1) (-3)
-21/-3 = n -1
7 = n-1
n = 8

8th term is 0 in this AP.

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hope it helps ^_^

Answer 2

$a = 21 \\ d = 18 - 21 = 15 - 18 = - 3 \\ tn \: = \: a + (n - 1)d \\ \: \: \: \: \: = 21 + (n - 1)( - 3) \\ - 81 = 21 + (n - 1)( - 3) \\ - 102 = (n - 1)( - 3) \\ (n - 1) = \frac{102}{3} \\ (n - 1) = 34 \\ and \: n = 34 + 1 = 35 \\ now \: for \: tn \: to \: be \: 0 \: n = \\ 0 = 21 + (n - 1)( - 3) \\ - 21 = (n - 1)( - 3) \\ (n - 1) = 7 \\ n = 8.....the \\ 8th \: term \: will \: be \: 0 \: of \: this \: ap$