For an AP(arithmetic progression) if S49=100 and T50=25 then S50=____

Answers (1)

The given $$T 50 = 20

 and S 49 = 100

We know that the formula  $$ Tn = a +n(-1)d $$\ and $$ Sn = fracn2 [2a + (n-1)d] $$\

then                                   

                                              $$T50 = 25$$\ $$ a + 49 d = 25$$\ $$ a = 25 -49d ......(1)

and                         

                                               $$Sn = 100 $$\ $$ frac492[2(25 - 49d) + 48d] = 100 $$\ $$ 49[50 -98d + 48d] = 200$$\ $$ 2450 - 2450 d =200$$\ $$ d = frac45 49

Now putting this value in Equation (1)

                                        $$ a = 25 - frac4549 	imes 49 $$\ $$ a = 25 -45 $$\ $$ a = -20

Now                 $$ S50 = frac502 [-40 + 45]$$\ $$ S50 = 125

Hence, $$ S50 = 125 $$\

 

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