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Answer :
S10 = 4000. To determine the entries of the next row in Pascal's Triangle, we add adjacent terms from the current row.
Thus, the next row will be:
1 7 21 35 35 21 7 1
5a) The sequence has first term t1 = 9, and a common difference of d = 6. Then, the general term is given by tn = 6n + 3. Thus, t7 = 6(7) + 3 = 45.
5b) The sequence has first term t1 = 8192, and a common ratio of r = -2. Then, the general term is given by tn = 8192(-2)^(n-1). Thus, t11 = 8192(-2)^(10) = -8388608.
The series is an arithmetic series with first term a=800, common difference d=−600/3=−200, and number of terms n = 10. Thus, using the formula for the sum of an arithmetic series, we have:
S10 = (n/2)(a + tn) = (10/2)(800 + (800 + (n-1)d)) = 4000
Therefore, S10 = 4000.
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