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The first term of the infinite arithmetic sequence {an} is A1 = 93, and the tolerance D1 = - 7. The first term of the infinite arithmetic sequence {BN} is B1 = 17, and the tolerance D2 = 12, Then, how many items are there in these two sequences with equal values?
By title
93-7x>=17①
17+12y=0)
The solution has X
When the sequence {an} and {BN} are two infinite arithmetic sequences, the tolerance is D1 and D2 respectively. This paper proves that the sequence {an + BN} is arithmetic sequence, and finds its tolerance
An + BN - (an-1 + bn-1) = (an-an-1) + (bn-bn-1) = D1 + D2, so {an + BN} is an arithmetic sequence, and the tolerance is D1 + D2
If the sequence {an}, {BN} is an arithmetic sequence, and the tolerances are D1 and D2 respectively, is the sequence {A2N}, {an, 2bn) an arithmetic sequence? If so, what is the tolerance
If the sequence {an}, {BN} is an arithmetic sequence and the tolerance is D1 and D2 respectively, then {A2N}, {an, 2bn) is an arithmetic sequence? If so, what is the tolerance {A2N} is. A (2n) - A (2 (n-1)) = 2 * D1, {an ± 2bn} is. A (n + 1) ± 2B (n + 1) - (an ± 2bn) = (a (n + 1) - an)) ± (2B (n + 1) - (2bn) = D1 ± 2 * D2
The sequence {an}, {BN} are all arithmetic sequence, and the tolerance is D1 and D2 respectively. Then the tolerance of {an + qbn} (q is constant) can be reduced
The tolerance of {an + qbn} (q is constant) is: D1 + QD2
an=a1 + (n-1)d1
bn=b1+ (n-1)d2,qbn=qb1 + (n-1)qb2
Let CN = an + qbn
Then, CN = a1 + QB1 + (n-1) (D1 + QD2)
Therefore, for CN, it can be equivalent to C1 = a1 + QB1,
Tolerance d = D1 + QD2
Then, the tolerance of {an + qbn} (q is a constant) is: D1 + QD2
RELATED INFORMATIONS
- 1. If an = BN, find n
- 2. Let the sequence {an} be an equal ratio sequence, the sum of the first n terms is Sn, and S3 = 3a3, and find the value of the common ratio Q As above
- 3. It is known that the sum of the first n terms of the equal ratio sequence {an} is Sn, A4 equals 2A3, S2 equals 6. Find the general term formula of the sequence {an}
- 4. It is known that SN is the sum of the first n terms of the equal ratio sequence {an}, and S3, S9 and S6 are equal difference sequence A .A3+A6=A9 B.A3*A6=A9 C.A3+A6=2A9 D.A3*A6=A9^2 Ask for detailed explanation
- 5. The {an} is an equal ratio sequence composed of positive numbers, Sn is the sum of the first n terms, a2a4 = 1, S3 = 7, S5 =?
- 6. Let an be an equal ratio sequence composed of positive numbers. If the sum of the first n terms is known as a2a4 = |, S3 = 7, then S5 = |?
- 7. If Sn = 2N-1, then A8=______ ．
- 8. Given that the sum of the first n terms of a sequence an is Sn, and an = 3 ^ n + 2n, then SN is equal to
- 9. Given that the first n terms of an and Sn are equal to the square of n minus n plus 1, the general term formula of an is obtained
- 10. Let the first n terms and Sn = (- 1) ^ n (2n ^ 2 + 4N + 1) - 1 of sequence {an} 1, find the general term formula an of sequence {an} 2, record BN = (- 1) ^ n / an, find the first n terms and TN of the sequence {BN}
- 11. Let A1 and d be real numbers, the first term be A1, the sum of the first n terms of the arithmetic sequence {an} with tolerance d be Sn, satisfying s5s6 + 15 = 0, then the value range of D is______ ．
- 12. Let {an} be an arithmetic sequence with the first term of 3 and the tolerance of D, and {BN} be a sequence determined by BN = an + an + 1, then what are the first n terms of {BN} and Sn?
- 13. The known sequence an satisfies: an + 1-2an = 2 ^ n + 1, and A1 = 2 (1). It is proved that {an / 2 ^ n} is the key to find the sequence an of arithmetic sequence (2)
- 14. An is an arithmetic sequence, an = 13 + (n-1) 2. An = log2bn. It is proved that BN is an arithmetic sequence
- 15. Let one of {an} and {BN} be a convergent sequence and the other a divergent sequence. It is proved that {an ± BN} is a divergent sequence We also ask whether {anbn} and {an / BN} (BN ≠ 0} must be divergent sequences
- 16. Let the sequence {an} {BN} be Lim an BN = 0. If an is unbounded, then BN must be bounded. Is it correct? Why?
- 17. In the expansion of (1 + 2x) ^ n, let the sum of binomial coefficients of odd terms be the sum of the first n terms of an sequence and be Sn, then what is Liman / Sn equal to
- 18. If we know that in the expansion of (1 + ax) 6, the coefficient of X3 is equal to 160, then the real number a=______ ．
- 19. If the constant term in the expansion of binomial (1 / x-ax ^ 2) ^ 9 is - 21 / 2, then the real number a =? RT
- 20. In the expansion of binomial (2x + 6) ^ 6, what is the coefficient with x ^ 4 term