Question

determine the AP whose fifth term is 15 and the sum of its 3rd and 8th term is 34

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Answer 1

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Answer 2

Answer:

The series in the form -1,3,7 ...... .

Step-by-step explanation:

Formula

Airthmetic series is given by

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

Where $a_{n}$ is the nth term , n is the nth term and d is the common difference .

As given

The AP whose fifth term is 15 and the sum of its 3rd and 8th term is 34 .

Thus

$15= a_{1}+ (5-1)d$

$15= a_{1}+4d$

$34= a_{3}+a_{8}$

$34=a_{1}+(3-1)d+a_{1}+(8-1)d$

$34=2a_{1}+2d+7d$

$34=2a_{1}+9d$

Two equation becomes

$15= a_{1}+4d$

$34=2a_{1}+9d$

Multiply $15= a_{1}+4d$ by 2 and subtracted from $34=2a_{1}+9d$.

$34-30=2a_{1}-2a_{1}+9d-8d$

4 = d

Put the value of d in the equation

$15= a_{1}+4\times 4$

$15= a_{1}+16$

$-16+15= a_{1}$

$-1= a_{1}$

For $a_{2}$

$a_{2}= -1+ (2-1)4$

$a_{2}= -1+1\times 4$

$a_{2}= -1+4$

$a_{2}=3$

For  $a_{3}$

$a_{3}= -1+ (3-1)4$

$a_{3}= -1+2\times 4$

$a_{3}= -1+8$

$a_{3}=7$

Therefore the series in the form -1,3,7 ...... .