Okay, let's tackle these. Starting with number 7. Step 1: Find the first term, a, by calculating S₁. The sum of the first term is the first term itself. S₁ = 2(1)² − 1; S₁ = 2 − 1; a = 1 Step 2: Find the sum of the first two terms, S₂. S₂ = 2(2)² − 2; S₂ = 2(4) − 2; S₂ = 8 − 2; S₂ = 6; Step 3: Find the second term, T₂, using the relationship S₂ = T₁ + T₂. Since T₁ = a = 1: 6 = 1 + T₂; T₂ = 6 − 1; T₂ = 5; Step 4: Calculate the common difference, d, using d = T₂ − T₁. d = 5 − 1; d = 4 The first term is 1 and the common difference is 4.

Number 7-12 please

May 14, 2026Mathematics

ScanSolve AI Answer

Answer

1

4

Step-by-step solution

4 steps

Okay, let's tackle these. Starting with number 7.

Find the first term, $a$ , by calculating $S_1$ .
The sum of the first term is the first term itself.
$S_1 = 2(1)^2 - 1$ $S_1 = 2 - 1$ $a = 1$
Find the sum of the first two terms, $S_2$ .
$S_2 = 2(2)^2 - 2$ $S_2 = 2(4) - 2$ $S_2 = 8 - 2$ $S_2 = 6$
Find the second term, $T_2$ , using the relationship $S_2 = T_1 + T_2$ .
Since $T_1 = a = 1$ :
$6 = 1 + T_2$ $T_2 = 6 - 1$ $T_2 = 5$
Calculate the common difference, $d$ , using $d = T_2 - T_1$ .
$d = 5 - 1$ $d = 4$
The first term is $\boxed{1}$ and the common difference is $\boxed{4}$ .

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Number 7-12 please

Answer

Step-by-step solution

Find the first term, aaa, by calculating S1S_1S1​.

Find the sum of the first two terms, S2S_2S2​.

Find the second term, T2T_2T2​, using the relationship S2=T1+T2S_2 = T_1 + T_2S2​=T1​+T2​.

Calculate the common difference, ddd, using d=T2−T1d = T_2 - T_1d=T2​−T1​.

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More Mathematics Questions

Find the first term, $a$ , by calculating $S_1$ .

Find the sum of the first two terms, $S_2$ .

Find the second term, $T_2$ , using the relationship $S_2 = T_1 + T_2$ .

Calculate the common difference, $d$ , using $d = T_2 - T_1$ .