Math, asked by deradike26, 10 months ago

If the 9th term of an Arithmetic Progression(AP) is five times the 5th term, find the relationship between a and d.​

Answers

Answered by Anonymous
55

\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}

Using Formula of nth Term

Arithmetic Progression :-

{\boxed{\sf\:{a_{n}=a+(n-1)d}}}

Hence,

9th term will be :-

{\boxed{\sf\:{a_{n}=a+(n-1)d}}}

= a + (9 - 1)d

= a + 8d

5th Term will be :-

= a + (5 -1)d

= a + 4d

Given :-

\textbf{\underline{9th\;term\;of\;an\;AP\;is\;5\;times\; the\;5th\;term}}

Hence

9th term

a + 8d = 5(a + 4d)

a + 8d = 5a + 20d

a - 5a = 20d - 8d

-4a = 12d

{\boxed{\sf\:{\dfrac{-4a}{-4}=\dfrac{12d}{-4}}}}

Hence we get :-

a = -3d

\Large{\boxed{\sf\:{Relationship\;between\;a\;and\;d\;is \;(a = -3d)}}}

Answered by Anonymous
39

\boxed{\mathsf{\green{Answer}}}

a = -3d

\boxed{\mathsf{\green{Explanation}}}

Given:

In an A.P.

9th term = 5 times of 5th term

To Find:

Relationship between a and d

Solution:

let, the A.P. is

a, a+d, a+2d, a+3d... a+(n-1)d

Here,

a_1 = a

a_5 = a+4d

a_9 = a+8d

According to the question

a_9 = 5(a_5)

a+8d = 5(a+4d)

a+8d = 5a+20d)

5a-a = 8d - 20d

4a = -12d

a = -3d

\texttt{\blue{Aravind}\: \red{Reddy}....!}

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