Question

IF 7 TIMES THE 7TH TERM OF AN AP IS EQUAL TO 11 TIMES THE 11TH TERM, THEN FIND ITS 18TH TERM...
SOLVE IT FAST........ ​

Answer 1

Answer:

a18=0

Explanation:

let the first term be a

let the common difference be d

let the number of terms be n

According to question

7(a7)=11(a11)

as we know

an=a+(n-1)d

7(a+(7-1)d)=11(a+(11-1)d) [as n=7 on L.H.S and n=11. on R.H.S]

7(a+6d)=11(a+10d)

7a+42d=11a+110d

7a-11a=110d-42d

-4a=68d

a=68d/-4

a=-17d

a18=a+(n-1)d

a18=a+(18-1)d

a18=a+17d

a=-17d [proved above]

a18=-17d+17d

a18=0

Answer 2

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$\huge { \boxed{ \mathcal \pink{ \fcolorbox{red}{yellow}{answer}}}} \\ \\ 7(a7) = 11(a11) .................(1)\\ \\ \\ \\ a7 = a + 6d..........................(2) \\ \\ a11 = a + 10d..................(3) \\ \\ \\ put \: \: these \: values \: of \: equation \: (2) \: and \: \\ (3)rd \: in \: 1st \\ \\ \\ 7(a + 6d) = 11(a + 10d) \\ 7a + 42d = 11a + 110d \\ - 4a = 68d \\ \\ a = - 17d \\ now \\ a18 = a + 17d \\ a18 = - 17d + 17d \\ a18 = 0$