Question -
Answer -
(i) 10th termof the A.P. 1, 4, 7, 10, …..
Arithmetic Progression(AP) whose common difference is = an – an-1 wheren > 0
Let us consider, a = a1 =1, a2 = 4 …
So, Common difference,d = a2 – a1 = 4 – 1 = 3
To find the 10th termof A.P, firstly find an
By using the formula,
an = a+ (n-1) d
= 1 + (n-1) 3
= 1 + 3n – 3
= 3n – 2
When n = 10:
a10 =3(10) – 2
= 30 – 2
= 28
Hence, 10th termis 28.
(ii) 18th termof the A.P. √2, 3√2, 5√2, …
Arithmetic Progression(AP) whose common difference is = an – an-1 wheren > 0
Let us consider, a = a1 =√2, a2 = 3√2 …
So, Common difference,d = a2 – a1 = 3√2 – √2 = 2√2
To find the 18th termof A.P, firstly find an
By using the formula,
an = a+ (n-1) d
= √2 + (n – 1) 2√2
= √2 + 2√2n – 2√2
= 2√2n – √2
When n = 18:
a18 =2√2(18) – √2
= 36√2 – √2
= 35√2
Hence, 10th termis 35√2
(iii) nth term of the A.P13, 8, 3, -2, ….
Arithmetic Progression(AP) whose common difference is = an – an-1 wheren > 0
Let us consider, a = a1 =13, a2 = 8 …
So, Common difference,d = a2 – a1 = 8 – 13 = -5
To find the nth termof A.P, firstly find an
By using the formula,
an = a+ (n-1) d
= 13 + (n-1) (-5)
= 13 – 5n + 5
= 18 – 5n
Hence, nth termis 18 – 5n