Question

Find the 20h tem of an arithmetic progression 78, 80, 82, 84, 86...​

Answer 1

A n s w e r

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G i v e n

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• An AP 78, 80, 82, 84, 86....

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F i n d

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• 20th term of the AP

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S o l u t i o n

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We know that ,

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$\underline{\bold{\texttt{For nth term :}}}$

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➠ $\sf a_n = a + (n - 1)d$ ⚊⚊⚊⚊ ⓵

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Where ,

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• $\sf a_n$ = nth term

• a = First term

• n = Number of terms

• d = Common difference

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$\underline{\bold{\texttt{For 20th term of the given AP :}}}$

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• $\sf a_n = a_{20}$

• a = 78

• n = 20

• d = 80 - 78 = 2

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf a_n = a + (n - 1)d$

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➜ $\sf a_{20} = 78 + (20 - 1)2$

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➜ $\sf a_{20} = 78 + (19)2$

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➜ $\sf a_{20} = 78 + 38$

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➨ $\sf a_{20} = 116$

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• Hence the 20th term of the given AP is 116

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Additional information

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Sum of n terms

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• $\sf S_n = \dfrac { n } { 2 } (2a + (n - 1)d )$

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Where ,

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➻ $\sf S_n$ = Sum of n terms

➻ a = First term

➻ n = Number of terms

➻ d = Common difference

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Or ,

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• $\sf S_n = \dfrac { n } { 2 } (a + l)$

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Where ,

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➻ $\sf S_n$ = Sum of n terms

➻ a = First term

➻ n = Number of terms

➻ l = Last term or nth term

Answer 2

Question :

Find the 20 th term of an arithmetic progression 78 , 80, 84, 86..

Given :

• An arithmetic progression 78,80 ,84, 86,..

To find :

• 20th term of A.P

Solution :

Formula to be used :

$\boxed {\tt a_n = a + (n - 1)d}$

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where,

$\tt {a_n = nth \: term = ?}$

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$\tt { a = first \: term = 78 }$

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$\tt { n = number \: of \: terms \: = \: 20 }$

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$\tt { d = common \: difference \: = 2 }$

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$\small \mathfrak \pink{\underline {Putting \: the \: values \: in \: formula :}}$

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$:\implies \tt {a_n = a + (n - 1)d }$

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$: \implies \tt {a_{20} = 78 + ( 20- 1) 2}$

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$: \implies \tt { a_{20} = 78 + 38 }$

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$:\implies \tt {a_{20 }= 116 }$

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Hence, 20th term of A.P is 116