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Free sequence calculator for arithmetic and geometric sequences. Calculate nth term, sum of sequences, common difference, and common ratio with step-by-step solutions. Our math calculator helps you master sequences, series, and progressions for algebra and calculus.
Last updated: February 2, 2026
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Polar Coordinates:
In Radians:
0.9273 rad
In Degrees:
53.1301°
Calculation Steps:
Converting Rectangular to Polar Coordinates
Given: x = 3, y = 4
Step 1: Calculate r (radius)
r = √(3² + 4²) = 5.0000
Step 2: Calculate θ (angle)
θ = arctan(4/3) = 53.1301°
Conversion Formulas:
Formula
aₙ = a₁ + (n-1)d
Find any term using first term and common difference
Formula
aₙ = a₁ × r^(n-1)
Find any term using first term and common ratio
Method
Direct Calculation
Calculate the value of the nth term in any sequence
Arithmetic Sum
Sₙ = n/2(2a₁+(n-1)d)
Find the sum of arithmetic or geometric series
Pattern
0, 1, 1, 2, 3, 5, 8...
Each term is sum of previous two terms
Formula
d = aₙ - aₙ₋₁
Identify the constant difference between consecutive terms
Converting rectangular (3, 4) to polar coordinates:
Radius (r)
5.00
Angle (θ)
53.13°
Our sequence calculator uses fundamental mathematical formulas to calculate terms and sums of arithmetic and geometric sequences. The calculator applies proven sequence formulas to find any term, generate sequence values, and calculate series sums with precision.
Arithmetic Sequence:• nth term: aₙ = a₁ + (n-1)d• Sum: Sₙ = n/2 × (2a₁ + (n-1)d)Geometric Sequence:• nth term: aₙ = a₁ × r^(n-1)• Sum: Sₙ = a₁(1 - r^n) / (1 - r)These formulas are the foundation of sequence calculations. For arithmetic sequences, we add a constant difference; for geometric sequences, we multiply by a constant ratio. Our calculator handles both types and shows complete step-by-step solutions.
Shows arithmetic and geometric sequence patterns graphically
A sequence is an ordered list of numbers, while a series is the sum of sequence terms. Understanding the difference and pattern in sequences helps solve many mathematical and real-world problems involving regular patterns, growth, and progressions.
Need help with other math calculations? Check out our quadratic formula calculator and derivative calculator.
Get Custom Calculator for Your Math CourseResult: The 10th term is 29, and the sum of first 10 terms is 155
Sequence: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29
a₁ = 3, r = 2, find a₅
a₅ = 3 × 2⁴ = 3 × 16 = 48
Sum of 2, 6, 18, 54, 162
S₅ = 2(1-3⁵)/(1-3) = 242
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