Show work and explain with formulas.

10. find the sum (see picture).

11. find the sum of the geometric series: a_2 = -36, a_5 = 972, n = 7

12. find the first term: s_n = 315, a_n = 5, r = 1/2, n = 6

Step-by-step explanation:

10.

The formula of a sum of terms of a geometric sequence:

We have:

Therefore:

Substitute a₁ = 5, r = 2 and n = 9:

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11.

We have

We know:

Therefore

Substitute:

Calculate the first term:

Put a₁ = 12, r = -3 and n = 7 to the formula of a sum:

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12.

We have

We know:

Substitute:

Check for the given sum:

Substitute a₁ = 160, r = 1/2 and n = 6:

CORRECT :)

do you have a picture of the table