Question

Find sum of series 3÷2+3+9÷2+....27÷2

Answer 1

67.5

Explanation:

1.5 + 3 + 4.5 + ... + 13.5

In the first three terms, the common difference is 1.5, so this series is:

1.5 + 3 + 4.5 + 6 + 7.5 + 9 + 10.5 + 12 + 13.5

There are 9 terms.

1.5 + 3 + 4.5 + 6 + 7.5

+13.5 + 12 + 10.5 + 9

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15 + 15 + 15 + 15 + 7.5

1.5 + 3 + 4.5 + 6 + 7.5 + 9 + 10.5 + 12 + 13.5 = 4.5 × 15 = 67.5

You can also use the formula:

For an arithmetic series with n terms,

S_n = (n/2)(a_1 + a_n)

S_9 = (9/2)(1.5 + 13.5)

S_9 = 4.5(15)

S_9 = 67.5