Question

The sum of first 8 term of an ap is 100 and sum of first 19 term is 551 find ap

Answer 1

given

sum of first 8 terms of AP = 100

sum of first 19terms of AP = 551

Sn = 100, n = 8

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

100 = 8/2 [ 2a+ 8-1)d]

200 = 4 [ 2a + 7d]

200/4 = 25 = 2a + 7d _ (1)

Sn =551, n = 19

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

551 = 19/2[2a+ (19-1)d]

551×2/19 = 2a +19d

58 = 2a + 19d _ (2)

from eq (2) -(1) we get

33 = 11d

d = 33/11 = 3

substitute d in eq (1)

2a + 7×3 = 25

2a+ 21 = 25

2a = 21-25 =4

a = 4/2 = 2

a+d = 2+3 = 5

a+2d = 2 + 2×3 = 8

AP = 2, 5, 8, 11 ......

hope it helps you
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Answer 2

$\huge\bf\mathscr\pink{Your\: Answer}$

____________

____

2, 5, 8, 11, 14,...............

____

_____________

step-by-step explanation:

Let,

first term be 'a'

common difference be 'd'

Given,

sum of first 8 term of an ap is 100

and

sum of first 19 term is 551

On solving these equations,

( see the attachment)

we get,

2a + 7d = 25 .............(i)

2a + 18d = 58 ............(ii)

subtracting eqn (i) from (ii),

we get,

=> 18d - 7d = 58 - 25

=> 11d = 33

=> d = 33/11

=> d = 3

therefore,

from equation (i),

we get,

=> a = (25 - 7×3)/2

=> a = (25 - 21)/2

=> a = 4/2

=> a = 2

So,

the A.P is

2, 5, 8, 11, 14,...............