Question

Find the 31st term of an AP whose 4th term is 38 and 16th term is 73.​

Answer 1

Step-by-step explanation:

a+3d = 38. (4th term)

a+15d = 73. (16th term)

12 d = 35

d = 35/12

a = 38-(35/4) = 117/4

31 term = a+30d = 117/4 + 30*35/12 = 467/4

Answer 2

Answer:

467/4

Step-by-step explanation:

4th term= a₄=38                         16th term=a₁₆=73

HERE , n=4                                  HERE n=16

USING an=a+(n-1)*d                    USING an=a+(n-1)*d

            a₄=a+(4-1)*d                                 a₁₆=a+(16-1)*d

            a₄ =a+3d                                      a₁₆=a+15d

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NOW SUBTRACTING ,

 a+15d=73

 a+3d =38

(-)  (-)   = (-)

                 

12d=   35

   d=35/12

a+3d=38

a+3*35/12=38

a=38-35/4

a=152-35/4

a=117/4

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n=31

a₃₁=a+30d

    =117/4+30*35/12

    =117/4+175/2

    =117+350/4

    =467/4