SOLUTION: the kth term of a sequence is given by the functions (3^k) - 2k + 2. What is the sum of the first ten terms?

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Question 1191253: the kth term of a sequence is given by the functions (3^k) - 2k + 2. What is the sum of the first ten terms?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

first find the first ten terms:
a%5B1%5D=3%5E1+-+2%2A1+%2B+2=3
a%5B2%5D=3%5E2+-+2%2A2+%2B+2=7
a%5B3%5D=3%5E3+-+2%2A3+%2B+2=23
a%5B4%5D=3%5E4+-+2%2A4+%2B+2=75
a%5B5%5D=3%5E5+-+2%2A5+%2B+2=235
a%5B6%5D=3%5E6+-+2%2A6+%2B+2=719
a%5B7%5D=3%5E7+-+2%2A7+%2B+2=2175
a%5B8%5D=3%5E8+-+2%2A8+%2B+2=6547
a%5B9%5D=3%5E9+-+2%2A9+%2B+2=19667
a%5B10%5D=3%5E10+-+2%2A10+%2B+2=59031
sum=59031%2B19667%2B6547%2B2175%2B719%2B235%2B75%2B23%2B7%2B3=88482
sum%28%282+%2B+3%5Ek+-+2+k%29%2Ck=1%2C10%29=88482+

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Sum the separate parts of the expression separately, using summation formulas.



sum%28%283%5Ek%29%2Ck=1%2C10%29+=+%283-3%5E11%29%2F%281-3%29+=+88572 (use a calculator for that one)

sum%28%28-2k%29%2Ck=1%2C10%29+=+-2%28sum%28%28k%29%2Ck=1%2C10%29%29+=+-2%2855%29+=+-110

sum%28%282%29%2Ck=1%2C10%29+=+2%2810%29+=+20

ANSWER: 88572-110%2B20=88482