Answer :
The 100th and nth terms for the given sequence are found using the arithmetic sequence formula, resulting in 173+7*2^32 + (100-1)*2^32 for the 100th term, and 173+(6+n)*2^32 for the nth term.
The student is asking for the 100th and the nth term of a sequence. The given sequence consists of terms in the form of 173+k*232, where k starts from 7 and increments by 1 with each term.
To find the 100th or nth term, we can see that the sequence is arithmetic in nature as the difference between consecutive terms (due to the fixed 232 multiplier) is constant. Therefore, we use the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
In this case, a1 is 173+7*232 and d is 232. To find the 100th term, we substitute n with 100, and for the nth term, we keep n as is.
For example, the 100th term would be 173+7*232 + (100-1)*232.
For the nth term, it would be 173+(7+n-1)*232 which simplifies to 173+(6+n)*232.
