The first three terms of an AP respectively are $3y-1,\ 3y\ +5$ and $5y\ +1$.
Then y equals:
$( A) -3\ $
$ ( 8) \ 4$
$ ( C) \ 5$
$( D) \ 2$
Given: first three term of the A.P. $\displaystyle 3y-1,\ 3y+5\ and\ 5y+1\ $
To do: To find the value of y.
Solution:
The first three terms of an AP are$\displaystyle \ 3y-1,\ 3y+5\ and\ 5y+1$, respectively.
We need to find the value of y.
We know that if a, b and c are in AP,
Then $b-a=c-b$
$2b=a+c$
$2( 3y+5)=3y-1+5y+1$
$6y+10=8y$
$8y-6y=10$
$2y=10$
$y=\frac{10}{2}$
$y=5$
Hence, The correct option is $( C)$ .
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