IPMAT Indore 2019Algebra > Hard31323029✅ Correct Option: 1Related questions:If the sum of the first 212121 terms of the sequence: lnab,lnabb,lnab2,lnab2b,…\ln \frac{a}{b}, \ln \frac{a}{b \sqrt{b}}, \ln \frac{a}{b^{2}}, \ln \frac{a}{b^{2} \sqrt{b}}, \ldotslnba,lnbba,lnb2a,lnb2ba,… is lnambn\ln \frac{a^{m}}{b^{n}}lnbnam, then the value of m+nm+nm+n is \qquadThe 3rd ,14th 3^{\text {rd }}, 14^{\text {th }}3rd ,14th and 69th 69^{\text {th }}69th terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the nth n^{\text {th }}nth term of the arithmetic progression, then nnn equals ________.There are numbers a1,a2,a3,…,ana_1, a_2, a_3, \ldots, a_na1,a2,a3,…,an each of them being +1+1+1 or −1-1−1. If it is known that a1a2+a2a3+a3a4+…an−1an+ana1=0a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0a1a2+a2a3+a3a4+…an−1an+ana1=0 then