پلانز

حسابی ترتیب کیلکولیٹر (nواں رکن اور مجموعہ)

یہ کیلکولیٹر ایسی ترتیب کا nواں رکن اور پہلے n ارکان کا مجموعہ نکالتا ہے جو ہر بار ایک ہی مقدار سے بڑھتی یا گھٹتی ہے۔ پہلا رکن، مشترک فرق اور n درج کریں۔

نتیجہ

قدریں درج کریں اور نتیجہ دیکھنے کے لیے “حساب کریں” دبائیں۔

فارمولا

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.

یہ کیلکولیٹر کیسے استعمال کریں

  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.

حل شدہ مثالیں

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.

عام غلطیاں

  • 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.

اکثر پوچھے گئے سوالات

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 + …).