Find:
(i) 10th term of the A.P. 1,4,7,10,...
(ii) 18th term of the A.P. √2,3√2,5√2,...
(iii) nth term of the A.P. 13,8,3,-2,...
(iv) 10th term of the A.P. -40,-15,10,35,...
(v) 8th term of the A.P. 117,104,91,78,...
(vi) 11th term of the A.P. 10.0,10.5,11.0,11.5,..
(vii) 9th term of the A.P.3/4,5/4,7/4,9/4,...
Answers
Step-by-step explanation:
1) the number are added by 3
2)number before square root are odd number
3)the number are subtracted by 5
4)all number is added by 25
5)the number are subtracted by 13
6)the number are added by 0.5
7)odd number is divided by 4
ARITHMETIC PROGRESSIONS
1. A.P. = 1,4,7,10,...
a = 1
d = 4-1 = 3
a10 = a + 9d = 1 + (9*3) = 1 + 27 = 28
2. A.P. = √2,3√2,5√2,...
a = √2
d = 3√2 - √2 = 2√2
a18 = a + 17d = √2 + (17*2√2) = √2 + 34√2 = 35√2
3. A.P. = 13,8,3,-2,...
a = 13
d = - 5
an = a + (n-1)d = 13 + (-5(n-1)) = 13 - 5n + 5 = 18 - 5n
4. A.P. = -40,-15,10,35,...
a = - 40
d = -15 + 40 = 25
a10 = a + 9d = - 40 + (9*25) = - 40 + 225 = 185
5. A.P. = 117,104,91,78,...
a = 117
d = 104 - 117 = - 13
a8 = a + 7d = 117 + 7(-13) = 117 - 91 = 26
6. A.P. = 10.0,10.5,11.0,11.5,..
a = 10.0
d = 10.5 - 10.0 = 0.5
a11 = a + 10d = 10 + (10*0.5) = 10 + 5 = 15
7. A.P. = 3/4,5/4,7/4,9/4,...
a = 3/4
d = 5/4 - 3/4 = 2/4 = 1/2
a9 = a + 8d = 3/4 + (8*1/2) = 3/4 + 4 = 19/4