Question

Which term of ap 21,18,15.... is-42?

Answer 1

Answer:

22 th term

Step-by-step explanation:

d = 18 - 21 = -3

a = 21

nth term = a + (n-1)d

-42 = 21 + (n-1) (-3)

-42 = 21 - 3n + 3

3n = 66

n = 22

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Answer 2

$\underline\mathfrak{Given:-}$

• $\: \: \: \: \: An \: \: Ap \: \: given \: \: as \: \: {21}, \: {18}, \: {15}, ......$

$\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: Which \: \: terms \: \: of \: \: Ap \: \: {-42}.?$

$\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: Ap \: \: {21}, \: {18}, \: {15}, ......$

• $\: \: \: \: \: First \: \: terms \: \: = \: \: {21}$

• $\: \: \: \: \: Common \: \: difference \: \: = \: \: {18} \: - \: {21} \: \: = \: \: {-3}$

$\: \: \: \: \: \fbox{{A_n} \: \: = \: \: {a} \: + \: {(n \: - \: {1})} \: d }$

$\: \: \: \: \: \leadsto {42} \: \: = \: \: {21} \: + \: {(n \: - \: {1})} \: {-3}$

$\: \: \: \: \: \leadsto {42} \: - \: {21} \: \: = \: \: {(n \: - \: {1})} \: {-3}$

$\: \: \: \: \: \leadsto {-63} \: \: = \: \: {(n \: - \: {1})} \: {-3}$

$\: \: \: \: \: \leadsto \dfrac{-63}{-3} \: \: = \: \: {n} \: - \: {1}$

$\: \: \: \: \: \leadsto {-21} \: \: = \: \: {n} \: - \: {1}$

$\: \: \: \: \: \leadsto {-n} \: \: = \: \: {-21} \: - \: {1}$

$\: \: \: \: \: \leadsto {-n} \: \: = \: \: {-22}$

$\: \: \: \: \: \leadsto {n} \: \: = \: \: {22}$

• $\: \: \: \: \: So, \: \: {22th} \: \: term \: \: is \: \: {-42}$

$\underline\mathfrak{Verification:-}$

$\: \: \: \: \: \leadsto {22th} \: \: term \: \: = \: \: {a} \: + \: {21d}$

$\: \: \: \: \: \leadsto {21} \: + \: {21} \: \times \: {-3}$

$\: \: \: \: \: \leadsto {21} \: + \: {-63}$

$\: \: \: \: \: \leadsto {-42}$

• $\: \: \: \: \: So, \: \: the \: \: {22th} \: \: term \: \: of \: \: Ap \: \: is \: \: {-42}.$

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