Answer:
[tex]a + a17 = 40 \\ a + a18 = 43 \\ a + (a + 16d) = 40 \\ a + (a + 17d) = 43 \\ 2a + 16d = 40 \\ 2a + 17d = 43 \\ 2a + 17d - 2a - 16d = 43 - 40 \\ d = 3[/tex]
a+16d=40
a+16(3)=40
a+48=40
a=-8
a7=10
a11=22
a7+a11=32
a9=a+8d
a9=16
This problem is interesting!
a) The Common difference is 3
b) Sum of 7th and 11th terms is 40
c) 9th term is 20
STEP BY STEP EXPLAINTION :
Let [tex]tn[/tex] and [tex]d[/tex] be the nth term and common difference of AP respectively.
Given:
[tex]t1+t17=40-(1)[/tex]
[tex]t1+t18=43-(2)[/tex]
(A) Common difference
Subtracting eqn. (1) from (2),
[tex]t18-t17=43-40[/tex]
[tex]d=3[/tex]
B) Sum of 7th and 11th terms
From eqn. (1),
[tex]t1+t1+16d=40[/tex]
[tex]2t1+16d=40-(3)[/tex]
Now,
[tex]t7+t11=(t1+6d)+(t1+10d)=2t1+16d[/tex]
Using eqn. (3),
[tex]t7+t11=40[/tex]
C) 9th term
[tex]t9=t7+t11/2[/tex]
[tex]t9[/tex] [tex]=40/2[/tex]
[tex]t9[/tex] [tex]=20[/tex]
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Answers & Comments
Answer:
[tex]a + a17 = 40 \\ a + a18 = 43 \\ a + (a + 16d) = 40 \\ a + (a + 17d) = 43 \\ 2a + 16d = 40 \\ 2a + 17d = 43 \\ 2a + 17d - 2a - 16d = 43 - 40 \\ d = 3[/tex]
a+16d=40
a+16(3)=40
a+48=40
a=-8
a7=10
a11=22
a7+a11=32
a9=a+8d
a9=16
Verified answer
This problem is interesting!
Answer:
a) The Common difference is 3
b) Sum of 7th and 11th terms is 40
c) 9th term is 20
STEP BY STEP EXPLAINTION :
Let [tex]tn[/tex] and [tex]d[/tex] be the nth term and common difference of AP respectively.
Given:
[tex]t1+t17=40-(1)[/tex]
[tex]t1+t18=43-(2)[/tex]
(A) Common difference
Subtracting eqn. (1) from (2),
[tex]t18-t17=43-40[/tex]
[tex]d=3[/tex]
B) Sum of 7th and 11th terms
From eqn. (1),
[tex]t1+t1+16d=40[/tex]
[tex]2t1+16d=40-(3)[/tex]
Now,
[tex]t7+t11=(t1+6d)+(t1+10d)=2t1+16d[/tex]
Using eqn. (3),
[tex]t7+t11=40[/tex]
C) 9th term
[tex]t9=t7+t11/2[/tex]
[tex]t9[/tex] [tex]=40/2[/tex]
[tex]t9[/tex] [tex]=20[/tex]