The sum of first 7 terms of an ap is 119 and that of first 17 terms is 714 find the sum of first nterms
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let first term be a and common diffrence be d
now,
S7 = 7/2(2a+(7-1)d)
119 = 7/2(2a+6d)
119 = 7/2*2(a+3d)
119/7 = a+3d
17=a+3d .........................(1)
Also,
S17 = 17/2(2a+(17-1)d
714 = 17/2*2(a+8d)
714/17 = a+8d
42 = a+8d..........................(2)
Subtracting (1) from (2)
42-17 = a+3d-a-8d
25 = -5d
d = -5
putting d= -5 in (1)
17 = a+ 3(-5)
17 = a-15
17+15 = a
a = 32
Now, a= 32 , d= -5
Sn = n/2{2Γ32+ (n-1)-5}
Sn = n/2(64-5n+5)
Sn = n/2(69-5n)
Sn = 69n/2 - 5n^2/2
hope it will help
now,
S7 = 7/2(2a+(7-1)d)
119 = 7/2(2a+6d)
119 = 7/2*2(a+3d)
119/7 = a+3d
17=a+3d .........................(1)
Also,
S17 = 17/2(2a+(17-1)d
714 = 17/2*2(a+8d)
714/17 = a+8d
42 = a+8d..........................(2)
Subtracting (1) from (2)
42-17 = a+3d-a-8d
25 = -5d
d = -5
putting d= -5 in (1)
17 = a+ 3(-5)
17 = a-15
17+15 = a
a = 32
Now, a= 32 , d= -5
Sn = n/2{2Γ32+ (n-1)-5}
Sn = n/2(64-5n+5)
Sn = n/2(69-5n)
Sn = 69n/2 - 5n^2/2
hope it will help
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