Respuesta :
Answer:
I will be happy to help you with that! Here is the corrected version of the text with improved clarity:
(i) For this arithmetic progression (A.P.),
a = 2
a3 = 26
We know that the formula for the nth term of an arithmetic progression is an = a + (n - 1)d.
Substituting a3 and an into the formula, we get:
a3 = a + 2d
26 = 2 + 2d
d = 12
Using the formula for a2, we get:
a2 = a + d
a2 = 2 + 12
a2 = 14
Therefore, the missing term is 14.
(ii) For this A.P.,
a2 = 13
a4 = 3
Using the formula for the nth term of an arithmetic progression, we get:
a2 = a + d
13 = a + d ... (i)
a4 = a + 3d
3 = a + 3d ... (ii)
Subtracting (i) from (ii), we get:
-10 = 2d
d = -5
Substituting d into (i), we get:
13 = a - 5
a = 18
Using the formula for a3, we get:
a3 = a + 2d
a3 = 18 + 2(-5)
a3 = 8
Therefore, the missing terms are 18 and 8, respectively.
(iii) For this A.P.,
a1 = 5
a4 = 912
Using the formula for the nth term of an arithmetic progression, we get:
a4 = a + 3d
912 = 5 + 3d
d = 32
Using the formula for a2, we get:
a2 = a + d
a2 = 5 + 32
a2 = 37
Using the formula for a3, we get:
a3 = a2 + d
a3 = 37 + 32
a3 = 69
Therefore, the missing terms are 37 and 69, respectively.
(iv) For this A.P.,
a = -4
a6 = 6
Using the formula for the nth term of an arithmetic progression, we get:
a6 = a + 5d
6 = -4 + 5d
d = 2
Using the formula for a2, we get:
a2 = a + d
a2 = -4 + 2
a2 = -2
Using the formula for a3, we get:
a3 = a + 2d
a3 = -4 + 2(2)
a3 = 0
Using the formula for a4, we get:
a4 = a + 3d
a4 = -4 + 3(2)
a4 = 2
Using the formula for a5, we get:
a5 = a + 4d
a5 = -4 + 4(2)
a5 = 4
Therefore, the missing terms are -2, 0, 2, and 4, respectively.
(v) For this A.P.,
a2 = 38
a6 = -22
Using the formula for the nth term of an arithmetic progression, we get:
a2 = a + d ... (i)
a6 = a + 5d ... (ii)
Subtracting (i) from (ii), we get:
-22 - 38 = 4d
-60 = 4d
d = -15
Substituting d into (i), we get:
a = a2 - d
a = 38 - (-15)
a = 53
Using the formula for a3, we get:
a3 = a + 2d
a3 = 53 + 2(-15)
a3 = 23
Using the formula for a4, we get:
a4 = a + 3d
a4 = 53 + 3(-15)
a4 = 8
Using the formula for a5, we get:
a5 = a + 4d
a5 = 53 + 4(-15)
a5 = -7
Therefore, the missing terms are 53, 23, 8, and -7, respectively.
Step-by-step explanation:
If I do not get brainlest for this I will freak out lol.
