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