Question

3 9 15 21 sequence is an ap if it is an ap then find the next two terms​

Answer 1

Given :-

An A.P sequence 3 , 9 , 15 , 21 , . . . .

To Find :-

Next two terms of the sequence

Solution :-

Before starting the answer , let's recall

An A.P is of the form :-

$\quad \leadsto \quad \sf a_{1} , a_{2} , a_{3} , \cdots \cdots , a_{n}$

or can also be written as ;

${\quad \leadsto \quad \sf a , a + d , a + 2d , \cdots \cdots , a + ( n - 1 )d}$

Also ,

• d = $\sf a_{2} - a_{1}$

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Now , Here ,

$\quad \leadsto \quad \sf A.P = 3 , 9 , 15 , 21 , . . . .$

Here ,

• a = 3
• d = 9 - 3 = 6

Now , We have to find 5th and 6th term let's find out ;

$\quad \leadsto \quad \sf a_{n} = a + ( n - 1 )d$

${ : \implies \quad \sf a_{5} = 3 + ( 5 - 1 ) 6}$

${ : \implies \quad \sf a_{5} = 3 + ( 4 ) 6}$

${ : \implies \quad \sf a_{5} = 3 + 24}$

${ : \implies \quad \bf \therefore \quad a_{5} = 27}$

Now , let's find 6th term ;

${ : \implies \quad \sf a_{6} = 3 + ( 6 - 1 ) 6}$

${ : \implies \quad \sf a_{6} = 3 + ( 5 ) 6}$

${ : \implies \quad \sf a_{6} = 3 + 30}$

${ : \implies \quad \bf \therefore \quad a_{6} = 33}$

Henceforth , The Required Answer is 5th term = 27 and 6th term = 33 :)