Geometric Sequence Calculator
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common difference (r) | |
Nth term to obtain |
Geometric Sequence
an = a x rn-1 OR r x a n-1
In a sequence if the ratio between every two consecutive term is constant then the sequence is known as " Geometric Sequence ".
- nth term (an ) = a x rn-1 (or) an = r x an-1
- Sum of the first n terms, Sn = a x (rn -1) / (r - 1) when r ≠ 1
and Sn = na when r = 1. - Sum of infinite terms, S∞ = a / (1 - r) when |r| < 1 and S∞ diverges
when |r| ≥ 1.
Suppose, 'a ' is the first number and 'r' is the common ratio, then the sequence is of the form a, ar, ar2, ar3, ....,
Example:
Find a15 of a geometric sequence if a13 = -8 and r = 1/3.
Solution:
By the formula of geometric sequence,
Find a15 of a geometric sequence if a13 = -8 and r = 1/3.
Solution:
By the formula of geometric sequence,
a14 = r a13 = (1/3) (-8) = -8/3
a 15 = r a14 = (1/3) (-8/3) = -8/9.
Therefore, a15 = -8/9.
a 15 = r a14 = (1/3) (-8/3) = -8/9.
Therefore, a15 = -8/9.