Question

Which term of the A.P.7/2,3/2,-1/2,.....is 337/2​

Answer 1

an=a+(n-1)d

337/2=7/2+(n-1)4/2

337-7/2=(n-1)4/2

330/2×2/4=n-1

82.5=n-1

n=83.5

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Answer 2

Correct Question :

Which term of the A.P.7/2,3/2,-1/2,.....is "-337/2​" ?

Answer :

87th term is -337/2

Step-by-step explanation :

$\underline{\bf Arithmetic \ Progression:}$

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• General form of AP,

      a , a+d , a+2d , a+3d , ..........

____________________________

Given A.P. series,

7/2 , 3/2 , -1/2 , ......

• first term, a = 7/2

• common difference,

   d = 3/2 - 7/2 = (3 - 7)/2 = -4/2 = -2

Let nth term be -337/2

• aₙ = -337/2

We have to find the value of "n"

We know,

nth term of an A.P is given by,

 $\boxed{\bf a_n=a+(n-1)d}$

$\rightarrow \frac{-337}{2} =\frac{7}{2} +(n-1)(-2) \\\\ \rightarrow \frac{-337}{2}-\frac{7}{2} =(n-1)(-2) \\\\ \rightarrow \frac{-337-7}{2} =(n-1)(-2) \\\\ \rightarrow \frac{-344}{2} =(n-1)(-2) \\\\ \rightarrow -172=-2n+2 \\\\ \rightarrow -172-2=-2n \\\\ \rightarrow -174=-2n \\\\ \rightarrow 2n=174 \\\\ \rightarrow n=174/2 \\\\ \rightarrow n=87$

87th term is -337/2