Paket

Kalkulator Barisan Aritmetika (Suku ke-n dan Jumlah)

Kalkulator ini mencari suku ke-n dan jumlah n suku pertama dari barisan yang naik atau turun dengan besar yang sama setiap kali. Masukkan suku pertama, beda, dan n.

Hasil

Masukkan nilai lalu ketuk Hitung untuk melihat hasilnya.

Rumus

an=a1+(n−1)da_n = a_1 + (n - 1)d

Start at the first term and add the difference n − 1 times.

Sn=n2(a1+an)S_n = \frac{n}{2}(a_1 + a_n)

The sum is the number of terms times the average of the first and last term.

Cara menggunakan kalkulator ini

  1. Enter the first term and the common difference (the amount added each time; negative if the sequence goes down).
  2. Enter n, the term you want (and how many terms to add).
  3. Press Calculate to see the nth term, the sum and the first few terms.

Contoh soal

3, 7, 11, 15, … : the 10th term and the sum of 10 terms

a₁₀ = 3 + 9 × 4 = 39.

S₁₀ = 10/2 × (3 + 39) = 5 × 42 = 210.

A decreasing sequence: 20, 17, 14, …

a₈ = 20 + 7 × (−3) = −1.

S₈ = 8/2 × (20 + (−1)) = 4 × 19 = 76.

The sum 1 + 2 + … + 100

a₁₀₀ = 100, so S₁₀₀ = 100/2 × (1 + 100) = 5050.

Kesalahan umum

  • Using n instead of n − 1 in the nth-term formula: the first term already counts as one.
  • Getting the sign of d wrong for a decreasing sequence.
  • Adding the terms with the sum formula but the wrong last term.

Pertanyaan umum

How do you find the nth term of an arithmetic sequence?

Use aₙ = a₁ + (n − 1)d. For 3, 7, 11, …: a₁ = 3 and d = 4, so aₙ = 3 + 4(n − 1) = 4n − 1.

How do you find the common difference?

Subtract any term from the next one: 7 − 3 = 4. It is the same for every pair in an arithmetic sequence.

What is the difference between an arithmetic sequence and series?

A sequence is the list of terms (3, 7, 11, …); a series is their sum (3 + 7 + 11 + …).