1,7,8,49,50,56,57,343,344,350,351,392,393,399,400
The above sequence contains sum of distinct power of 7 in increasing order(7^0,7^1,7^1+7^0,7^2 etc.) What is value of term number 38 ?

• 2nd term is 7^1
  4th term is 7^2
  8th term is 7^3
  so 16th term will be 7^4 and 32nd=7^5
  now as we see 3rd term=7+1
  5th term=49+1
  6th term=49+7
  7th term=49+8
  now,9th term=343+1
  10th=343+7
  11th=343+8
  12th=343+49 and so on..
  so, 33rd term=(7^5)+1=16808
  34th=16807+7
  35th=16807+8
  38th=16807+56=16863 (ans)
• 12 years agoHelpfull: Yes(26) No(17)
• akshay your soloution is wrong..clear your basics dont mislead..
  in these type of questions there is a trick
  as shown is series it is like
  7^0
  7^1
  7^0+7^1
  7^2
  7^0+7^2
  7^1+7^2
  .....
  hence last term in power five will be
  7^5+7^4+7^3+7^2+7^1+7^0 this is first method
  now second method is trick based that is we want 38 term directly solve like this
  so first number is 3 and second is 8 so gap is 8-3=5 when we calculate this polynomial hence ans is 7^3+7^5=17150..
  
  
  
• 12 years agoHelpfull: Yes(19) No(19)
• @akshay shut up and mind your language..
• 12 years agoHelpfull: Yes(6) No(7)
• @swati first see your language then tell me anything...so you shut up..
• 12 years agoHelpfull: Yes(6) No(6)
• It is very simple. Convert the number to binary. For example 5 = 101 in binary. So, the 5th term is 7^2 + 7^0 = 50 ignoring zeros of binary numbers. Another example 10 = 1010 in binary. So, the 10th term is 7^3 + 7^1 = 350. Now, 38 = 100110 in binary. So, 38th term = 7^5 + 7^2 + 7^1 = 16863.
• 12 years agoHelpfull: Yes(6) No(0)
• clearly we have pattern here.... the power term positions follow like
  for 38th value split it in the powers of 2 like
  38 = 32+6
  32+4+2
  then write as 2^5+2^2+2^0
  
  then just replace the 2 base with 7 number given that leads us to
  
  =7^5+7^2+7^0
  =16807+49+1
  =16857
  
  now we can do this method for any value series
  
• 12 years agoHelpfull: Yes(5) No(1)
• @ SWATI SINGH
  give your answer if u want dont judge anyone's answer...
  now i have given it with logic..
• 12 years agoHelpfull: Yes(3) No(7)
• answer is 7^5+7^2+7^1=16863
• 12 years agoHelpfull: Yes(3) No(0)
• akshay jain can u please explain how??
  
• 12 years agoHelpfull: Yes(2) No(3)
• ans -16863
• 12 years agoHelpfull: Yes(2) No(2)
• ans is=16978
• 12 years agoHelpfull: Yes(1) No(9)
• the 38th term will be 7^3+7^7=823886
• 12 years agoHelpfull: Yes(0) No(0)
• please send it today at sobhandutta@gmail.com
• 12 years agoHelpfull: Yes(0) No(0)
• In PRASANTH G KRISHNA solution I made the correction.
  
  clearly we have pattern here.... the power term positions follow like
  for 38th value split it in the powers of 2 like
  38 = 32+6
  32+4+2
  then write as 2^5+2^2+2^1
  
  then just replace the 2 base with 7 number given that leads us to
  
  =7^5+7^2+7^1
  =16807+49+7
  =16863
  
  now we can do this method for any value series
• 5 years agoHelpfull: Yes(0) No(0)