Final answer:
To calculate the sum of a sequence, determine if it's arithmetic or geometric to apply the appropriate formula or sum the terms individually. With a calculator like the TI-83, enter the sequence into the list and use the sum function, then round the answer according to significant figures.
Step-by-step explanation:
Step-by-Step Solution (Solution A)
To find the sum of a sequence without a calculator, it is important to first determine if the sequence follows a particular pattern such as arithmetic or geometric progression. For arithmetic sequences, you can use the formula S = n/2(a1 + an), where S is the sum, n is the number of terms, a1 is the first term, and an is the last term. For geometric sequences, the sum can be calculated using S = a1(1 - r^n) / (1 - r), where r is the common ratio. When sequences do not fall into these categories, you may need to sum the terms individually.
Using the TI-83, 83+, 84, 84+ Calculator (Solution B)
To use a calculator such as the TI-83, 83+, 84, or 84+ to find the sum of a sequence, you can enter the sequence into the list editor and use the built-in sum function. After calculating the sum, the calculator might show a decimal form like 2,001.06 as an answer. However, if the terms being summed have their farthest-right significant figure in the ones place, you must round your final answer to the ones position to ensure it aligns with the principles of significant figures. For instance, if you are summing the numbers 611 and 1027, the final answer must be presented as 1,638 not 1,638.00.