Q. 2 A4.1( 12 Votes )

# Find the sum of each of the following arithmetic series: Here, First term = 7

Common difference = d = (21/2) - 7 = (7/2)

Last term = l = 84

Now, 84 = a + (n - 1)d

84 = 7 + (n - 1)(7/2)

84 - 7 = (n - 1)(7/2)

77 = (n - 1)(7/2)

154 = 7n - 7 (multiplying both sides by 2)

154 + 7 = 7n

7n = 161

n = 23

there are 23 terms in this Arithmetic series.

Now, Sum of these 23 terms is given by

S23 = [2(7) + (23 - 1)(7/2)]

= (23/2) × [14 + (22)(7/2) ]

= (23/2) × [14 + 77]

= (23/2) × 

= 2093/2

= 1046.5

Thus, sum of 23 terms of this AP is 1046.5.

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