Question

1 ,7 ,8 ,49 ,50 ,56 ,57 ,343 ,344 ,350 ,351 ,392 ,393 ,399 ,400 ,…….. The above sequence contains sums of distinct powers of 7 in the increasing order (7^0, 7^1, 7^1 + 7^0, 7^2, etc). What is the value of term number 36?

Answer 1

Answer:

16856

Step-by-step explanation:

Given 1 ,7 ,8 ,49 ,50 ,56 ,57 ,343 ,344 ,350 ,351 ,392 ,393 ,399 ,400 ,…….. The above sequence contains sums of distinct powers of 7 in the increasing order (7^0, 7^1, 7^1 + 7^0, 7^2, etc). What is the value of term number 36?

Now seven power is present in 1st, 2nd,4th, 8th, 16th, 32nd, 64th. Power of 7 will be 0,1,2,3,4,5,6

Now term 1,2,4,8,16,32 = power to 7-----------(1)

We need to find 38 th term

38 th term = 32 th term + 6 th term

By eqn 1 , 32 th term = 7^5 and 6 th term is 56

So 36 th term = 7^5 + 49 = 16856

= 16856

So we can do it as

32nd term = 7^5

33 rd term = 7^5 + 1

34 th term = 7^5 + 7

35 th term = 7^5 + 8

36 th term = 7^5 + 49  = 16,856