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
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
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= 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.
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.