Solve the equation 1×2-8=0 / 2. The formula for nth term Progression is Rn-3. (i) Find one first term (ii)…

Question

Solve the equation 1×2-8=0 / 2. The formula for nth term Progression is Rn-3. (i) Find one first term (ii) Find the common difference of 7 terms is 48.

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Here are the solutions to your problems. Problem 1: Solve the equation 1x² − 8 = 0 Step 1: Isolate the x² term. x² − 8 = 0; x² = 8 Step 2: Take the square root of both sides. Remember to include both positive and negative roots. x = ±√(8); x = ±√(4 × 2); x = ± 2√(2); The solutions are x = 2√(2) or x = −2√(2). Problem 2: Arithmetic Progression The formula for the n^(th) term of an arithmetic progression is T_n = 2n−3. i) Find the first term Step 1: To find the first term, substitute n=1 into the formula for T_n. T₁ = 2(1) − 3; T₁ = 2 − 3; T₁ = −1 The first term is −1. ii) Find the common difference if the sum of 5 terms is 45. Step 1: We use the first term a = T₁ = −1 found in part (i). We are given n=5 and S₅ = 45. The formula for the sum of the first n terms of an arithmetic progression is: S_n = n/2(2a + (n−1)d) Step 2: Substitute the known values into the sum formula. 45 = 5/2(2(−1) + (5−1)d); 45 = 5/2(−2 + 4d) Step 3: Solve for d. Multiply both sides by 2: 45 × 2 = 5(−2 + 4d); 90 = 5(−2 + 4d) Divide both sides by 5: 90/5 = −2 + 4d; 18 = −2 + 4d Add 2 to both sides: 18 + 2 = 4d; 20 = 4d Divide by 4: d = 20/4; d = 5 The common difference is 5.

Solve the equation 1x2−8=0 / 2. The formula for nth term Progression is Rn-3. (i) Find one first term (ii) Find the common difference of 7 terms is 48.

Answers

Step-by-step solution

Part i· 1 step

To find the first term, substitute $n=1$ into the formula for $T_n$ .

Part ii· 3 steps5

We use the first term $a = T_1 = -1$ found in part (i).

Substitute the known values into the sum formula.

Solve for $d$ .

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