1. Insert 3 arithmetic means between -24 & -12
2. Insert 3 arithmetic means between 15 & 31
3. Insert 4 arithmetic means between -6 & 29
4. Insert 4 arithmetic means between 7 & -13
5. Insert 5 arithmetic means between -18 & 24
6. Insert 5 arithmetic means between 11 & 47
7. Insert 6 arithmetic means between -9 & 40
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Answer:
1. -24, -21, -18, -15, -12
2. 15, 19, 23, 27, 31
3. -6, 1, 8, 15, 22, 29
4. 7, 3, -1, -5, -9, -14
5. -18, -11, -4, 3, 10, 17, 24
6. 11, 17, 23, 29, 35, 41, 47
7. -9, -2, 5, 12, 19, 26, 33, 40
Step-by-step explanation:
1. Given:
d=? a1=-24 n=5
an=a1+(n-1)d
-12=-24+(5-1)d
-12+24=5d-d
12=4d ÷ 4
d=3
-24, -21, -18, -15, -12
2. Given:
d=? a1=15 n=5
an=a1+(n-1)d
31=15+(5-1)d
31-15=5d-d
16=4d ÷ 4
d=4
15, 19, 23, 27, 31
3. Given:
d=? a1=-6 n=6
an=a1+(n-1)d
29=-6+(6-1)d
29+6=6d-d
35=5d ÷ 5
d=7
-6, 1, 8, 15, 22, 29
4. Given:
d=? a1=7 n=6
an=a1+(n-1)d
-13=7+(6-1)d
-13-7=6d-d
-20=5d ÷ 5
d=-4
7, 3, -1, -5, -9, -14
5. Given:
d=? a1=-18 n=7
an=a1+(n-1)d
24=-18+(7-1)d
24+18=7d-d
42=6d ÷ 6
d=7
-18, -11, -4, 3, 10, 17, 24
6. Given:
d=? a1=11 n=7
an=a1+(n-1)d
47=11+(7-1)d
47-11=7d-d
36=6d ÷ 6
d=6
11, 17, 23, 29, 35, 41, 47
7. Given:
d=? a1=-9 n=8
an=a1+(n-1)d
40=-9+(8-1)d
40+9=8d-d
49=7d ÷ 7
d=7
-9, -2, 5, 12, 19, 26, 33, 40