## Arithmetic Series Worksheet Solution2

In the page arithmetic series worksheet solution2 you are going to see solution of each questions from the arithmetic series worksheet.

(ii) 6 + 5 ¼ + 4 ½ + ......... 25 terms

Solution:

In this series we have 25 terms so n = 25

a = 6      d = t₂ - t₁

= 5 ¼ - 6

= (21/4)  - 6

= (21-24)/4

d = -3/4

Sn = (n/2) [ 2a + (n-1) d ]

S₂₅ = (25/2) [ 2(6) + (25-1) (-3/4) ]

= (25/2) [ 12 + (24) (-3/4) ]

= (25/2) [ 12 + (6) (-3) ]

= (25/2) [ 12 - 18 ]

= (25/2) [ -6 ]

= (25) [ -3 ]

= -75

(4) Find the sum of each arithmetic series described

(i) a = 5 n = 30 and L = 121

Solution:

S n = (n/2) [ a+ L ]

= (30/2) [ 5 + 121 ]

= (15) [126]

S₃₀ = 1890

(ii) a = 50    n = 25    and d = -4

Solution:

S n = (n/2) [ 2a + (n-1) d ]

S₂₅ = (25/2) [ 2(50) + (25-1) (-4) ]

= (25/2) [ 100 + (24) (-4) ]

= (25/2) [ 100 - 96 ]

= (25/2) [4]

= (25) [2]

= 50

(5) Find the sum of first 40 terms of the series

1² - 2² + 3² - 4²  + ........

Solution:

=  1² - 2² + 3² - 4²  + ........ 40 terms

= (1 - 4) + (9 - 16)  + ........ 20 terms

= - 3 - 7 + ........ 20 terms

here a = -3   d = -7 - (-3)   n = 20

= -7 + 3

d = -4

S n = (n/2) [ 2a + (n-1) d ]

= (20/2) [ 2(-3) + (20-1) (-4)]

= 10 [ -6 + 19 (-4)]

= 10 [ -6 + 19 (-4)]

= 10 [ -6 -76]

= 10 [ -82]

= -820

(6) In an arithmetic series,the sum of first 11 terms is 44 and the that of the next 11 terms is 55. Find the arithmetic series.

Solution:

Sum of first 11 terms = 44

S₁₁ = 44

(11/2)[2a + (11-1) d] = 44

2a + 10 d = (44 x 2)/11

2a + 10 d = 4 x 2

2 a + 10 d = 8   ----- (1)

Sum of next 11 term = 55

S₂₂ = S₁₁ + 55

S₂₂ = 44 + 55

S₂₂ = 99

(22/2)[2a + (22-1) d] = 99

2a + 21 d = (99 x 2)/22

2a + 21 d = 9

2 a + 21 d = 9   ----- (2)

Solving (1) and (2) we get

-11 d = -1

d = 1/11

Substitute d = 1/11 in the first  equation we get

2 a + 10 (1/11) = 8

2 a + 10/11 = 8

2 a  = 8 - (10/11)

2 a  = (88 - 10)/11

2 a  = 78/11

a  = 78/(2x11)

a = 39/11

Therefore the series is (39/11) + (40/11) + (41/11) + ............

These are the contents in the page arithmetic series worksheet solution2.
arithmetic series worksheet solution2