Arithmetic Series and Sigma Notation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Adding arithmetic runs with sigma

Mathematics · Algebra · ages 17-18
Name ______________________   Date ____________

  1. What is the sum of the integers from 1 to 50?

    • 1275
    • 1250
    • 1300
    • 1225

  2. Ana says pairing 1 to 100 gives pairs that each sum to 100. Is Ana right?

    Circle one:   True   False

  3. What is the value of the sum of (2k + 1) for k = 1 to 4?

    Answer: ______________

  4. What is the sum of the integers from 1 to 50?

    • 1275
    • 1250
    • 1300

  5. What is the sum of the first 100 even numbers, 2 + 4 + ... + 200?

    Answer: ______________

  6. What is the sum of the first 100 even numbers, 2 + 4 + ... + 200?

    Answer: ______________

  7. An arithmetic sequence starts 3, 7, 11, ... What is the sum of its first 20 terms?

    Answer: ______________

  8. An arithmetic sequence starts 3, 7, 11, ... What is the sum of its first 20 terms?

    Answer: ______________

  9. Tom says pairing 1 to 50 gives 50 pairs of 51. What is wrong?

    • Each pair sums to 50, not 51
    • Pairing only works for adding 1 to 100
    • There are 25 pairs, not 50, so the total is 1275

  10. What is the sum of the first 50 odd numbers?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_bAIPng87JO-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Adding arithmetic runs with sigma W1-mt_bAIPng87JO-s1

  1. 1275 · Pair 1 with 50, 2 with 49, and so on. Each pair sums to 51, and there are 25 pairs, so 25 times 51 is 1275.
  2. False · Each pair sums to 101, like 1 + 100 and 2 + 99. So Ana is wrong.
  3. 24 · Putting k = 1, 2, 3, 4 gives 3, 5, 7, 9. They add to 24.
  4. 1275 · Pair 1 with 50, 2 with 49, and so on into 25 pairs of 51. That gives 25 times 51 = 1275.
  5. 10100 · Factor 2 out to get twice the sum 1 to 100. That is 2 times 5050 = 10100.
  6. 10100 · Factor out 2 to get twice the sum 1 to 100, which is 2 times 5050, giving 10100.
  7. 820 · The sequence has first term 3 and common difference 4, so S = 10 times (6 plus 76), which is 820.
  8. 820 · The 20th term is 79, so pairs of 3 + 79 = 82 come 10 times. That gives 820.
  9. There are 25 pairs, not 50, so the total is 1275 · 50 numbers make 25 pairs, not 50. The sum is 25 times 51 = 1275.
  10. 2500 · Pair 1 with 99, 3 with 97, and so on into 25 pairs of 100. That gives 2500.
Worksheet · LightMySky