please solve ques 16,17,18,19 20 its very urgent and important 20 21 12 Find A 14 - Maths - Sequences and Series

Question

please
solve ques 16,17,18,19&20 its very urgent and important

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

17 Let terms of A P be a-d,a,a+d and that of G P be AR,A,AR Given
thatSum of A P
=126⇒a-d+a+a+d=126⇒3a=126⇒a=42Second term of A P
+Second Term of G P =76⇒a+A=76⇒42+A=76⇒A=34First
term of A P +First Term of G P
=85⇒a-d+AR=85⇒42-d+34R=85⇒34R-d=43 ;iThird term
of A P +Third Term of G P
=84⇒a+d+AR=84⇒42+d+34R=84⇒34R+d=42
;iiii+i⇒34R+d+34R-d=42+43⇒34R+1R=85⇒34R2+1R=85⇒34R2-85R+34=0Dividing
each term by 17 we
get,2R2-5R+2=0⇒2R2-4R-R+2=0⇒2RR-2-1R-2=0⇒2R-1R-2=0⇒R=12
or R=2When R=2 and A=34, we
haveAR,A,AR=342,34,34×2=17,34,68When R=12 and A=34, we
haveAR,A,AR=3412,34,34×12=68,34,17Hence we will get same
numbers for both values of R, just the order is reversed Put R=2 in
i,342-d=43⇒d=17-43⇒d=-26We have a=42 and d=-26,
hencea-d,a,a+d=42--26,42,42-26=68,42,16Put R=12 in
i,3412-d=43⇒d=68-43⇒d=25We have a=42 and d=25,
hencea-d,a,a+d=42-25,42,42+25=17,42,67Hence Numbers in A P are
68,42,16 and numbers in G P are 17,34,68 ORNumbers in A P are
17,42,67 and numbers in G P are 68,34,17
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