Mipango

Kikokotoo cha Mfuatano wa Hesabu (Kipengee cha n na Jumla)

Kikokotoo hiki kinatafuta kipengee cha n na jumla ya vipengee n vya kwanza vya mfuatano unaopanda au kushuka kwa kiasi kilekile kila mara. Weka kipengee cha kwanza, tofauti ya pamoja na n.

Tokeo

Weka thamani kisha bonyeza Kokotoa ili kuona tokeo.

Fomula

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.

Jinsi ya kutumia kikokotoo hiki

  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.

Mifano iliyotatuliwa

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.

Makosa ya kawaida

  • 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.

Maswali yanayoulizwa mara kwa mara

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 + …).