Question

6. Show that the sequence 9,12,15,18 ........ is an AP.Find its 15t term and the
general term.​

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Answer 1

Answer:

15th term = 51

Step-by-step explanation:

Yes, it's an ap,because

12-9=3

15-12=3

and d=3 in all the stage.

now, the general term...

note that the nth term ,means the formula an=a+(n-1)d is also known as the general term.

so, an=9+(n-1)3

= 9 +3n-3

=6+3n......(1)

Now, 15th term....

a15=9 + 14×3

=9+42

=51.... (2)

Answer 2

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Given:}}}}$

The AP are 9, 12 , 15, 18........15th term

$\large{\underline{\red{\rm{To\:Find:}}}}$

The 15th term of AP

$\large{\underline{\green{\rm{Let:}}}}$

The 1st term of AP (a)=9

The common difference=a²-a¹=12-9=3

$\small{\underline{\purple{\rm{As\:per\:the\:Ap:}}}}$

$\large{\boxed{\green{\rm{T_n=a+(n-1)d:}}}}$

$\sf{\longrightarrow T_1_5=9+(15-1)3}$

$\sf{\longrightarrow T_1_5=9+14*3}$

$\sf{\longrightarrow T_1_5=9+42}$

$\sf{\longrightarrow T_1_5=51}$

Hence,

$\sf\purple{\longrightarrow The\:15th\:term\:AP=51}$