Question -
Answer -
(i)┬аWhich term of the A.P.3, 8, 13,тАж is 248 ?
Given A.P is 3, 8,13,тАж
Here, a1┬а=a = 3, a2┬а= 8
Common difference, d =a2┬атАУ a1┬а= 8 тАУ 3 = 5
We know, an┬а=a + (n тАУ 1)d
an┬а= 3+ (n тАУ 1)5
= 3 + 5n тАУ 5
= 5n тАУ 2
Now, to find whichterm of A.P is 248
Put an┬а=248
тИ┤┬а5n тАУ 2 = 248
= 248 + 2
= 250
= 250/5
= 50
Hence, 50th┬аtermof given A.P is 248.
(ii)┬аWhich term of the A.P.84, 80, 76,тАж is 0 ?
Given A.P is 84, 80,76,тАж
Here, a1┬а=a = 84, a2┬а= 88
Common difference, d =a2┬атАУ a1┬а= 80 тАУ 84 = -4
We know, an┬а=a + (n тАУ 1)d
an┬а=84 + (n тАУ 1)-4
= 84 тАУ 4n + 4
= 88 тАУ 4n
Now, to find whichterm of A.P is 0
Put an┬а=0
88 тАУ 4n = 0
-4n = -88
n = 88/4
= 22
Hence, 22nd┬аtermof given A.P is 0.
(iii)┬аWhich term of the A.P.4, 9, 14,тАж is 254 ?
Given A.P is 4, 9,14,тАж
Here, a1┬а=a = 4, a2┬а= 9
Common difference, d =a2┬атАУ a1┬а= 9 тАУ 4 = 5
We know, an┬а=a + (n тАУ 1)d
an┬а= 4+ (n тАУ 1)5
= 4 + 5n тАУ 5
= 5n тАУ 1
Now, to find whichterm of A.P is 254
Put an┬а=254
5n тАУ 1 = 254
5n = 254 + 1
5n = 255
n = 255/5
= 51
Hence, 51st┬аtermof given A.P is 254.