SOLUTION: SUM OF 8TH TERM OF A.P IS 160 WHILE THE SUM OF 20TH TERM IS 800.FIND THE 43TERM AND THE SUM OF THE 12TERM.

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Question 946510: SUM OF 8TH TERM OF A.P IS 160 WHILE THE SUM OF 20TH TERM IS 800.FIND THE 43TERM AND THE SUM OF THE 12TERM.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
S%5B8%5D=160
S%5B8%5D=%288%2F2%29%28a%5B1%5D%2Ba%5B8%5D%29=160
a%5B1%5D%2Ba%5B8%5D=40
a%5B1%5D%2Ba%5B1%5D%2Bd%288-1%29=40
1.2a%5B1%5D%2B7d=40
.
.
S%5B20%5D=800
S%5B20%5D=%2820%2F2%29%28a%5B1%5D%2Ba%5B20%5D%29=800
a%5B1%5D%2Ba%5B20%5D=80
a%5B1%5D%2Ba%5B1%5D%2Bd%2820-1%29=80
2.2a%5B1%5D%2B19d=80
Subtract eq.1 from eq. 2,
2a%5B1%5D%2B19d-2a%5B1%5D-7d=80-40
12d=40
d=40%2F12
d=10%2F3
and
2a%5B1%5D%2B19%2810%2F3%29=80
2a%5B1%5D=80-190%2F3
2a%5B1%5D=240%2F3-190%2F3
2a%5B1%5D=50%2F3
a%5B1%5D=25%2F3
So then,
a%5B43%5D=a%5B1%5D%2Bd%2843-1%29
a%5B43%5D=25%2F3%2B%2810%2F3%29%2842%29
a%5B43%5D=25%2F3%2B420%2F3
highlight%28a%5B43%5D=445%2F3%29
.
.
.
S%5B12%5D=%2812%2F2%29%28a%5B1%5D%2Ba%5B12%5D%29
S%5B12%5D=6%2825%2F3%2B25%2F3%2B%2810%2F3%29%2811%29%29
S%5B12%5D=6%2825%2F3%2B25%2F3%2B110%2F3%29
S%5B12%5D=6%28160%2F3%29
highlight_green%28S%5B12%5D=320%29