UAUL,(ii) The sum of the 4th and 8th term of an A.P. is 54 and their p

1.	UAUL,(ii) The sum of the 4th and 8th term of an A.P. is 54 and their product is 665. Find the sum of the first 30 termof the A.P. (The terms of the AP are in ascending order)
Answer» Answer: 1920 Step-by-step EXPLANATION: A4+A8=54 a+3d+a+7d=54 2A+10d=54 a+5d=27 a=27-5d ____eq.1 A4×A8=665 (a+3d)(a+7d) = 665 (27-5d+3d)(27-5d+7d)=665 (27-2d)(27+2d)=665 729+54d-54d-4d^2=665 -4d^2=665-729 -4d^2=-64 d^2=16 d=4 PUT the VALUE of d in eq.1 a=27-5×4 a=26-20 a=6 a=6,d=4,n=30 Sn=n/2[2a+(n-1)d] S30=30/2[2×6+(30-1)×4] S30=30/2[12+116] S30=30/2×128 S30=30×64 S30=1920

UAUL,(ii) The sum of the 4th and 8th term of an A.P. is 54 and their product is 665. Find the sum of the first 30 termof the A.P. (The terms of the AP are in ascending order)

Answer»

Answer:

1920

Step-by-step EXPLANATION:

A4+A8=54

a+3d+a+7d=54

2A+10d=54

a+5d=27

a=27-5d ____eq.1

A4×A8=665

(a+3d)(a+7d) = 665

(27-5d+3d)(27-5d+7d)=665

(27-2d)(27+2d)=665

729+54d-54d-4d^2=665

-4d^2=665-729

-4d^2=-64

d^2=16

d=4

PUT the VALUE of d in eq.1

a=27-5×4

a=26-20

a=6

a=6,d=4,n=30

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

S30=30/2[2×6+(30-1)×4]

S30=30/2[12+116]

S30=30/2×128

S30=30×64

S30=1920

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UAUL,(ii) The sum of the 4th and 8th term of an A.P. is 54 and their product is 665. Find the sum of the first 30 termof the A.P. (The terms of the AP are in ascending order)​

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UAUL,(ii) The sum of the 4th and 8th term of an A.P. is 54 and their product is 665. Find the sum of the first 30 termof the A.P. (The terms of the AP are in ascending order)