Question -
Answer -
LetтАЩs consider a1,a2, тАж am┬аbe┬аm┬аnumbers suchthat 1, a1, a2, тАж am, 31 is an A.P.
And here,
a┬а= 1,┬аb┬а= 31,┬аn┬а=┬аm┬а+2
So, 31 = 1 + (m┬а+2 тАУ 1) (d)
30 = (m┬а+1)┬аd
d = 30/ (m + 1) тАжтАж.(1)
Now,
a1┬а=┬аa┬а+┬аd
a2┬а=┬аa┬а+2d
a3┬а=┬аa┬а+3d┬атАж
Hence, a7┬а=┬аa┬а+7d
amтАУ1┬а=┬аa┬а+(m┬атАУ 1)┬аd
According to thequestion, we have
Therefore, the valueof m is 14.