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What does the "S" stand for? How do I find a1 and d?

What does the "S" stand for? How do I find a1 and d?-example-1
User Nick Rassadin
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1 Answer

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22 votes

Answer

a₁ = 4

d = -3

Step-by-step explanation

a₇ = -14

S₇ = -35

using aₙ = a₁ + (n-1)d

a₇ = a₁ + (7 -1)d

a₇ = a₁ + 6d

substitute a₇ = -14, we have

-14 = a₁ + 6d

a₁ + 6d = -14 --------(i)

Sₙ = n/2[2a₁ + (n-1)d]

S₇ ⇒ n = 7

S₇ = 7/2[2a₁ + (7 - 1)d]

Substitute S₇ = -35, we have

-35 = 7/2[2a₁ + 6d]

Cross multiplying and opening the bracket yields

7(2a₁ + 6d) = -70

Divide both sides by 7

2a₁ + 6d = -70/7

2a₁ + 6d = -10 -------(ii)

Comparing equation (i) and (ii) and substract (i) from (ii)

a₁ + 6d = -14 --------(i)

2a₁ + 6d = -10 -------(ii)

2a₁ - a₁ = -10 - (-14)

a₁ = -10 + 14

a₁ = 4

To find d, substitute a₁ = 4 into equation (i)

Recall (i) a₁ + 6d = -14

4 + 6d = -14

6d = -14 - 4

6d = -18

d = -18/6

d = -3

User Kickinchicken
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