Question

if 6 times th 6th term of an A.P. is equal to 9 times the 9th tarm, show that it's 15th term is zero.​

Answer 1

6 times 6th term of an AP is equal to 9 times 9th term.

So we have,

$\longrightarrow 6\cdot a_6=9\cdot a_9\quad\quad\dots(1)$

6th term of an AP is,

$\longrightarrow a_6=a+5d$

and 9th term is,

$\longrightarrow a_9=a+8d$

where $a$ is first term and $d$ is common difference.

Then (1) becomes,

$\longrightarrow 6(a+5d)=9(a+8d)$

$\longrightarrow 6a+30d=9a+72d$

$\longrightarrow9a-6a+72d-30d=0$

$\longrightarrow3a+42d=0$

$\longrightarrow3(a+14d)=0$

$\longrightarrow a+14d=0$

$\longrightarrow\underline{\underline{a_{15}=0}}$

I.e., the 15 term of the AP is zero.

Hence Proved!

Answer 2

Answer:

Step-by-step explanation:

6a*6=9a*9

6(a+5d)=9(a+8d)

6a+30d=9a+72d

6a-9a=72d-30

-3a=42d

a/d=-42/3

a=-42

d=3

a*15=a+14d

=-42+42

=0.