Question

solve the attachment​

Answer 1

Answer:

$for AP:</p><p>term1 = a</p><p>term3 = a+2d</p><p>term9 = a+8d</p><p>but term7 = 19 = a+6d</p><p>so a = 19-6d</p><p></p><p>so re-defining:</p><p>term1 = 19-6d</p><p>term3 = 19-6d+2d = 19-4d</p><p>term9 = 19-6d + 8d = 19+2d</p><p></p><p>these 3 are supposed to be a GP, so</p><p>(19-4d)/(19-6d)= (19+2d)/(19-4d)</p><p>361 - 152d + 16d^2 = 361 -76d - 12d^2</p><p>28d^2 - 76d = 0</p><p>d(28d - 76) = 0</p><p>d = 0 or d = 76/28 = 19/7</p><p></p><p>case1 (trivial case) , d = 0</p><p>then all terms in the AP would be 19</p><p>i.e. 19 19 19 19 ...</p><p>of course the first 3 would be a GP also , etc</p><p></p><p>case 2:</p><p>d = 19/7</p><p>a = 19 - 6d = 19-6(19/7) = 19/7</p><p></p><p>for AP, term 20 = a+19d = 19/7+19(19/7) = 380/7</p><p></p><p>now term1 of AP = term1 of GP</p><p>a of GP = 19/7</p><p>term 3 of AP = term2 of GP</p><p>term2 of GP = a+2d = 19/7 + 2(19/7) = 57/7</p><p>so r of GP = (57/7) ÷ (19/7) = 3</p><p></p><p>sum 12 of GP = a(r^12 - 1)/r</p><p>= (19/7)(3^12 - 1)/2</p><p>$

Answer 2

Answer:

here's your answer

Explanation:

for AP: < /p > < p > term1 = a < /p > < p > term3 = a+2d < /p > < p > term9 = a+8d < /p > < p > but term7 = 19 = a+6d < /p > < p > so a = 19-6d < /p > < p > < /p > < p > so re-defining: < /p > < p > term1 = 19-6d < /p > < p > term3 = 19-6d+2d = 19-4d < /p > < p > term9 = 19-6d + 8d = 19+2d < /p > < p > < /p > < p > these 3 are supposed to be a GP, so < /p > < p > (19-4d)/(19-6d)= (19+2d)/(19-4d) < /p > < p > 361 - 152d + 16d^2 = 361 -76d - 12d^2 < /p > < p > 28d^2 - 76d = 0 < /p > < p > d(28d - 76) = 0 < /p > < p > d = 0 or d = 76/28 = 19/7 < /p > < p > < /p > < p > case1 (trivial case) , d = 0 < /p > < p > then all terms in the AP would be 19 < /p > < p > i.e. 19 19 19 19 ... < /p > < p > of course the first 3 would be a GP also , etc < /p > < p > < /p > < p > case 2: < /p > < p > d = 19/7 < /p > < p > a = 19 - 6d = 19-6(19/7) = 19/7 < /p > < p > < /p > < p > for AP, term 20 = a+19d = 19/7+19(19/7) = 380/7 < /p > < p > < /p > < p > now term1 of AP = term1 of GP < /p > < p > a of GP = 19/7 < /p > < p > term 3 of AP = term2 of GP < /p > < p > term2 of GP = a+2d = 19/7 + 2(19/7) = 57/7 < /p > < p > so r of GP = (57/7) ÷ (19/7) = 3 < /p > < p > < /p > < p > sum 12 of GP = a(r^12 - 1)/r < /p > < p > = (19/7)(3^12 - 1)/2 < /p > < p >forAP:</p><p>term1=a</p><p>term3=a+2d</p><p>term9=a+8d</p><p>butterm7=19=a+6d</p><p>soa=19−6d</p><p></p><p>sore−defining:</p><p>term1=19−6d</p><p>term3=19−6d+2d=19−4d</p><p>term9=19−6d+8d=19+2d</p><p></p><p>these3aresupposedtobeaGP,so</p><p>(19−4d)/(19−6d)=(19+2d)/(19−4d)</p><p>361−152d+16d2=361−76d−12d2</p><p>28d2−76d=0</p><p>d(28d−76)=0</p><p>d=0ord=76/28=19/7</p><p></p><p>case1(trivialcase),d=0</p><p>thenalltermsintheAPwouldbe19</p><p>i.e.19191919...</p><p>ofcoursethefirst3wouldbeaGPalso,etc</p><p></p><p>case2:</p><p>d=19/7</p><p>a=19−6d=19−6(19/7)=19/7</p><p></p><p>forAP,term20=a+19d=19/7+19(19/7)=380/7</p><p></p><p>nowterm1ofAP=term1ofGP</p><p>aofGP=19/7</p><p>term3ofAP=term2ofGP</p><p>term2ofGP=a+2d=19/7+2(19/7)=57/7</p><p>sorofGP=(57/7)÷(19/7)=3</p><p></p><p>sum12ofGP=a(r12−1)/r</p><p>=(19/7)(312−