Question

naina made a 10 layer multi strand ornament for her friend Diana. She used 45 beads for the first layer, 42 beads in the 2nd layer and 39 beads in the third layer. how many total beads did naina use to complete the ornament

Answer 1

The answer to your problem is, 1260

Explanation:

Well we know she made 10 “ strand ornaments “ for each layers we would need to add;

45 + 42 + 39

= 126

We would actually then need to multiply it by 10. Shown:

126 × 10

= 1260

Thus the answer to your problem is, 1260

Answer 2

To find the total number of beads Naina used to complete the ornament, we need to sum the number of beads in each layer.

Total number of beads = 45 + 42 + 39 + ... (continue the pattern until the 10th layer)

Notice that the number of beads in each layer decreases by 3. We can use arithmetic series formula to find the sum of the beads in all 10 layers:

S = (n/2) x (a + l)

where S is the sum, n is the number of terms, a is the first term, and l is the last term.

Here, a = 45, l = 18 (since the 10th layer will have 18 beads), and n = 10 (since there are 10 layers). Thus, we have:

S = (10/2) x (45 + 18) = 5 x 63 = 315

Therefore, Naina used a total of 315 beads to complete the ornament.