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algol13
2 years ago
9

Which expression represents the value of the series below? 3+ 7 + 11 + 15 + ... + 1,671

Mathematics
1 answer:
torisob [31]2 years ago
4 0

Answer:

Step-by-step explanation:

This is an Arithmetic Series with common difference 4 and first term 3

so the nth term an = 3 + (n -1)4

= 4n - 1.

The sum of n terms

= n/2 (a1 + L)

= n/2(3 + 1671)

=  837n.

There are (1671-3) / 4 + 1 = 418 terms in the series,

so the total value of the series is 837*418

= 349,866.

.

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Step-by-step explanation:

1st year interest calculated = 3.25/100 × $4500/1 = $146.25

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3rd year principal = 2nd principal + 2nd year interest = $4646.25 + $151 = $4797.25. 3rd year interest calculated = 3.25/100 × $4797.25/1 = $155.91

4th year principal = 3rd year principal + 3rd year interest =$4797.25 + $155.91 =$4953.16. 4th year principal calculated = 3.25/100 × 4953.16/1 =$160.98

5th year principal = 4th year principal + 4 year interest = &4953.16 +$160.98 = $5114.14. 5th year interest calculated = 3.25/100 × 5114.14/1 =$166.21

6th year principal =5th year principal + 5th year interest = $5114.14 + $166.21 =$5280.35. 6th year interest calculated = 3.25/100 × 5280.35/1 =$171.61

Amount = main principal + compound interest =$4500 +&146.25 +$151+$155.91+$160.98+$166.21+$171.61 =$5451.96

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