(In reply to

Answer by K Sengupta)

Let the ith term of the given sequence be denoted by T(i).

Substituting i = 1,2,3,4,5,... in turn, we observe that the value of the sequence i*T(i) is: 2, 5,_, 17, 28,.....

Now, 5 = 2+3, and we note that 2 is the 1st prime and 3 is the second prime. Similarly:

17 = 2+3+5+7

28 = 2+3+5+7+11, and so on

Thus we can now assert that, the sequence i*T(i) corresponds to the sum of the first i primes.

We are required to find the 3rd, 6th and 7th terms.

Now,

3*T(3) = The sum of the first three primes is 2+3+5 = 10,

so that: T(3) = 10/3 = 3.33.....

6*T(6) = The sum of the first six primes is 41, so that:

T(6) = 41/6 = 6.833.....

7*T(7) = The sum of the first seven primes is 58, so that:

T(7) = 58/7 = 8.285714.....