50th term of the sequence 16,48,96,160,_____ is ?

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Please find below the solution to the asked query:

16,48,96,160,....48-16=3296-48=48160-96=64which means difference of terms is in A.P with common differencei.e. d=16 and first term=a=32How do we third term?Third term=First Term+Sum of terms upto third termi.e.96=16+32+48How do we get fourth term?Fourth=First Term+Sum of differences upto fourth term160=16+32+48+64Similarly T50=First term+Sum of differences upto 49th term=16+32+48+64+.....49th term   =16+4922a+49-1d  SumA.P.=n22a+n-1d=16+4922×32+48×16=16+492832=16+20384=20400 Answer

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Here the difference is in A.P
32,48,64          49 terms
Sum=1st term+sum of all the differences
sum of the diff.=49/2{32+(48*16)}=19600
Sum of given series=16+19600=19616
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