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Third term of an A.P. Is 16 and 7^{th} term is 12 more than 5^

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Third term of an $A . P .$ Is $16$ and $7^{t h}$ term is $12$ more than $5^{t h}$ term, then find $A P$ .

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Third term of an

A . P .

16

and

7^{t h}

term is

12

more than

5^{t h}

term, then find

A P

12 mins ago

Discuss this question LIVE

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Text solutionVerified

Let first term of

A . P .

a

and common difference is

d

and we know that nth term,

a_{n} = a + (n - 1) d

Given

a_{3} = 16

a + (3 - 1) d = 16

\Rightarrow a + 2 d = 16 ... (i)

According to question,

a_{7} = 12 - a_{5}

\Rightarrow a_{7} - a_{5} = 12

[a + (7 - 1) d] - [a + (5 - 1) d] = 12

\Rightarrow a_{7} + 6 d - a - 4 d = 12

\Rightarrow a + 6 d - a - 4 d = 12

\Rightarrow 2 d = 12

d = \frac{12}{2} = 6

Substituting value of

d

in equation

(i)

a + 2 (6) = 16

∴ a = 16 - 12 = 4

A P . a, a + d, a + 2 d, ...

= 4, 4 + 6, 4 + 2 \times 6, ....

= 4, 10, 16, ....

Hence, required

A . P .

4, 10, 16, 22, ...

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Question Text	Third term of an $A . P .$ Is $16$ and $7^{t h}$ term is $12$ more than $5^{t h}$ term, then find $A P$ .
Answer Type	Text solution:1
Upvotes	150