Question

the sum of a series of terms in AP is 128 if the first term is 2 and the last term is 14 find the common difference

Answer 1

Heya!
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Given that ,
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◾First term A => 2

◾ Last term L => 14

◾Sum of N terms Sn=> 128

Now , Sn = n/2 ( a + l )

128 = n/2 ( 2 + 14 )

256 = 16 N

N = 16

Hence Number of terms n => 16
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Now we can use the second formula for Sn=> n/2 ( 2a + ( n-1 ) d )

128 = 16/2 ( 4 + 15d )

16 = 4 + 15d

15d = 12

d=> 12/15

d=> 4/5
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Answer 2

Hii There!!!


Given, Sn = 128 , a = 2 , an = l = 14 , d = ?

Here firstly we have to find no. of terms i.e, 'n'

Since, Sn = n/2 [ a + l ]

=> 128 = n/2 [ 2 + 14 ]

=> 128 = n/2 [16]

=> 128 = 8n

=> n = 128 / 8

=> n = 16 terms


Now, We know that, an = a + ( n - 1 ) × d

=> 14 = 2 + ( 16 - 1 ) × d

=> 14 - 2 = 15 × d

=> 12 = 15 × d

=> d = 12/15

=> d = 4/5



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Hope it helps