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1. The general term of an A. P.
a, a + d, a + 2d, ... is given by tn = a + (n –1) d
2. Sn, the sum of the first n terms of an A. P.
a, a + d, a + 2d, ... is given by 
3. A sequence in which the difference of two cousecutive terms is always constant ( ≠ 0) is called an Arithmetic Progression (A. P.)
tn = Sn – Sn – 1
4. An arithmetic mean between a and b is (a + b)/2
5. A sequence in which the ratio of two consecutive terms is always constant ( ≠ 0) is called a Geometric Progression (G. P.)
6. The nth term of a G.P.: a, ar, ar2, ... is arn – 1
7. Sum of the first n terms of a G. P.: a, ar, ar2, ... is
8. The sums of an infintite G. P. a, ar, ar2, ... is given by
9. Geometric mean G between two numbers a and b is √ab
10. The arithmetic mean A between two numbers a and b is always greater than the corresponding Geometric mean G i.e., A > G.
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FAQs on Formula's Summary - Sequence and Series - Quantitative Aptitude for CA Foundation
| 1. What is the formula for the sum of an arithmetic series? |  |
| 2. How do you find the nth term of an arithmetic sequence? | |
Ans. The nth term of an arithmetic sequence can be found using the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
| 3. What is the formula for the sum of a geometric series? | |
Ans. The formula for the sum of a geometric series is given by Sn = a(1 - r^n)/(1 - r), where Sn is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
| 4. How do you find the nth term of a geometric sequence? | |
Ans. The nth term of a geometric sequence can be found using the formula an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
| 5. What is the difference between an arithmetic sequence and a geometric sequence? | |
Ans. In an arithmetic sequence, each term is obtained by adding a common difference to the previous term, while in a geometric sequence, each term is obtained by multiplying the previous term by a common ratio.
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