Geometric series

Geometric series

A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.
Basic concepts: Arithmetic series, Geometric sequences,
Related concepts: Pascal's triangle, Binomial theorem, Introduction to infinite series, Convergence & divergence of geometric series ,

Lessons

• the sum of n terms of a geometric series:
sn=t1(rn−1)r−1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}
=r⋅tn−t1r−1=\frac{r \cdot t_{n}-t_{1}}{r-1}
  • 1.
    Geometric series formula:sn=t1(rn−1)r−1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}
    Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … .
  • 2.
    Geometric series formula: sn=r⋅tn−t1r−1s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}
    Determine the sum of the geometric series: 8 + 2 + 12\frac{1}{2} + …. + 1512\frac{1}{{512}} .
  • 3.
    A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?
Do better in math today
Get Started Now
24.
Sequences and Series
24.1
Arithmetic sequences
24.2
Arithmetic series
24.3
Geometric sequences
24.4
Geometric series
24.5
Infinite geometric series
24.6
Sigma notation
24.7
Arithmetic mean vs. Geometric mean
AU Maths Methods
Don't just watch, practice makes perfect.