Asked by Anonymous

the sum of the first 8 terms of an A.P is 80 and sum of the next 4 terms 88 determine the A.P
Answered by Bosnian
a1 = initial term of A.P.

d = common difference

an = a1 + ( n - 1 ) d = nth term of the sequence

a8 = a1 + ( 8 - 1 ) d

a8 = a1 + 7 d

Sum of the n members in A.P:

Sn = n ( a1 + an ) / 2

S8 = 8 ( a1 + a8 ) / 2 = 80

( 8 / 2 ) ( a1 + a1 + 7 d ) = 80

4 ( 2 a1 + 7 d ) = 80

Divide both sides by 4

2 a1 + 7 d = 20

Next 4 terms in A.P:

a9 = a1 + 8 d

a10 = a1 + 9 d

a11 = a1 + 10 d

a12 = a1 + 11 d

Their sum is:

a9 + a10 + a11 + a12 = 88

a1 + 8 d + a1 + 9 d + a1 + 10 d + a1 + 11 d = 88

4 a1 + 38 d = 88

Now you must solve sysytem of two equation with two unknow:

2 a1 + 7 d = 20

4 a1 + 38 d = 88

Try that.

Solution: a1 = 3 , d = 2
Answered by Ikupsan
Correct
Answered by Emmanuel
Great
Answered by Feranmi
👍
Answered by Oloshi
= initial term of A.P.

d = common difference

an = a1 + ( n - 1 ) d = nth term of the sequence

a8 = a1 + ( 8 - 1 ) d

a8 = a1 + 7 d

Sum of the n members in A.P:

Sn = n ( a1 + an ) / 2

S8 = 8 ( a1 + a8 ) / 2 = 80

( 8 / 2 ) ( a1 + a1 + 7 d ) = 80

4 ( 2 a1 + 7 d ) = 80

Divide both sides by 4

2 a1 + 7 d = 20

Next 4 terms in A.P:

a9 = a1 + 8 d

a10 = a1 + 9 d

a11 = a1 + 10 d

a12 = a1 + 11 d

Their sum is:

a9 + a10 + a11 + a12 = 88

a1 + 8 d + a1 + 9 d + a1 + 10 d + a1 + 11 d = 88

4 a1 + 38 d = 88

Now you must solve sysytem of two equation with two unknow:

2 a1 + 7 d = 20

4 a1 + 38 d = 88

Try that.
There are no AI answers yet. The ability to request AI answers is coming soon!