Question

heyy u all answer fast no 5 all

Answer 1

Hey Friend
Here is your number

Here all the sums will be solved by authentic progression.
(i) 1 + 3 + 5 + 7
a = 1
d = 3 - 1 = 2
a(n) = 7
a(n) = a + (n - 1) d
7 = 1 + (n - 1) 2
7 = 1 + 2n - 2
7 = 2n - 1
7 + 1 = 2n
8 = 2n
8/2 = n
4 = n
n = 4
S(n) = n/2 [ 2a + (n - 1) d ]
= 4/2 [ 2 * 1 + (4 - 1) 2 ]
= 2 (2 + 3 * 2)
= 2 (2 + 6)
= 2 * 8
= 16
(ii) 1 + 3 + 5 + 7 + 9 + 11
a = 1
d = 3 - 1 = 2
a(n) = 11
a(n) = a + (n - 1) d
11 = 1 + (n - 1) 2
11 = 1 + 2n - 2
11 = 2n - 1
11 + 1 = 2n
12 = 2n
12/2 = n
6 = n
n = 6
S(n) = n/2 [ 2a + (n - 1) d ]
= 6/2 [ 2 * 1 + (6 - 1) 2 ]
= 3 (2 + 5 * 2)
= 3 (2 + 10)
= 3 * 12
= 36
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
a = 1
d = 3 - 1 = 2
a(n) = 19
a(n) = a + (n - 1) d
19 = 1 + (n - 1) 2
19 = 1 + 2n - 2
19 = 2n - 1
19 + 1 = 2n
20 = 2n
20/2 = n
10 = n
n = 10
S(n) = n/2 [ 2a + (n - 1) d ]
= 10/2 [ 2 * 1 + (10 - 1) 2 ]
= 5 (2 + 9 * 2)
= 5 (2 + 18)
= 5 * 20
= 100

Hope this helped you
Have a nice day.