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Solving mathematical problems (sequence) in senior one The sum of the first n terms of sequence an is Sn, and satisfies an = - 3Sn × sn-1 (n ≥ 2), A1 = 1 / 3 (1) Verification: 1 / Sn is arithmetic sequence (2) Find the general term formula of sequence an
an=Sn-Sn-1=-3SnSn-1
Divide snsn-1 by both sides and get 1 / sn-1 / sn-1 = 3
So... Is an arithmetic sequence, the first term is 3, and the tolerance is 3
1/Sn=3+3(n-1)=3n
So Sn = 1 / 3N
Sn-1=1/(3n-3)
The two formulas are subtracted to obtain an = (n ≥ 2),
Then verify whether A1 meets the above equation
Mathematical sequence of senior one
Xiao Wang officially worked in a company in Beijing in January 2013. The company gave him a monthly salary of 5000 yuan. He wanted to use his spare time to increase his income. Assuming that the business work was also calculated from January, According to his requirements, the business income will increase at the rate of 50 yuan per month from 300 yuan. (1) what is his monthly income in the 12th month of the fifth year? (2) if 20% of Xiao Wang's total income is used for daily expenses, how many years later can he pay the down payment of 600000 yuan?
(1) D = 50, n = 12 * 5, A1 = 300, an = 300 + 12 * 5 * 50 = 3300; the twelfth month income of the fifth year = 5000 + 3300 = 8300 yuan
(2) Let n-th year (n * 5000 * 12 + 300 + n * 12 * 50) * (1-20%) ≥ 600000, then n ≥ 7497 / 672, n = 11.15625, rounded up to 12 years
Sequence (2 21:41:47)
Let the sum of the first n terms of the arithmetic sequence an be SN. If S4 ≥ 10 and S5 ≤ 15, then the maximum value of A4 is SN
D = 0, the maximum value of A4 is 3
3,3,3,3,3...
Is there such a formula in the equal ratio sequence? (28 22:41:45)
Is there such a formula? &# 160; &# 160; s3n = s2n + q2nsn
Yes, the following is the detailed derivation process: because: s3n = (1-Q ^ 3n) / (1-Q) * a1s2n = (1-Q ^ 2n) / (1-Q) * a1sn = (1-Q ^ n) / (1-Q) * A1, then: s3n = s2n + (Q ^ 2n-q ^ 3n) / (1-Q) * A1 = s2n + [Q ^ 2n * (1-Q ^ n)] / (1-Q) * A1 = s2n + Q ^ 2n * [(1-Q ^ n) / (1-Q) * A1] = s2n + Q ^ 2n * Sn
RELATED INFORMATIONS
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