Find the sum to 40 terms of the arithmetic sequence below. Please show your work. 14+23+32
1 answer:
Answer:
7580
Step-by-step explanation:
The formula for the sum of an arithmatic sequence is
,
where n = total number of terms (in this case 40)
= the first term (in this case 14)
and = the last term (we will need to find this)
to find the last term, we can use this formula:
where d is the difference between each term (in this case 9, because 23 - 14 = 9, and 32 - 23 = 9)
thus, = 14 + (40 - 1)9 = 14 + 39*9 = 14 + 351 = 365
plug this back into the first formula to get
Σ = (14 + 365) = 20(379) = 7580
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To find the volume of a dome, you would have to find the volume of the sphere, theoretically, and then divide it by two. To calculate the volume, we would use the formula 4/3 
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