Asked by Selena
The 4th term of an AP is 20 and the 8th term is 60. Find the 15th term
Answers
Answered by
R_scott
4 differences between 4th and 8th terms
(60 - 20) / 4 = 10 ... this is the common difference
(15 - 8) * 10 = 70
15th term = 8th term + 70
(60 - 20) / 4 = 10 ... this is the common difference
(15 - 8) * 10 = 70
15th term = 8th term + 70
Answered by
Bosnian
OR
an = a1 + ( n - 1 ) d
where
a1 = the initial term
d = the common difference of successive members
a4 = a1 + 3 d = 20
a8 = a1 + 7 d = 60
a8 - a4 = 60 - 20 = a1 + 7 d - ( a1 + 3 d )
40 = a1 + 7 d - a1 - 3 d
40 = a1 - a1 + 7 d - 3 d
40 = 4 d
d = 40 / 4
d = 10
Put this value in equation:
a1 + 3 d = 20
a1 + 3 ∙ 10 = 20
a1 + 30 = 20
Subtract 30 to both sides
a1 = - 10
a15 = a1 + 14 d
a15 = - 10 + 14 ∙ 10
a14 = - 10 + 140
a14 = 130
an = a1 + ( n - 1 ) d
where
a1 = the initial term
d = the common difference of successive members
a4 = a1 + 3 d = 20
a8 = a1 + 7 d = 60
a8 - a4 = 60 - 20 = a1 + 7 d - ( a1 + 3 d )
40 = a1 + 7 d - a1 - 3 d
40 = a1 - a1 + 7 d - 3 d
40 = 4 d
d = 40 / 4
d = 10
Put this value in equation:
a1 + 3 d = 20
a1 + 3 ∙ 10 = 20
a1 + 30 = 20
Subtract 30 to both sides
a1 = - 10
a15 = a1 + 14 d
a15 = - 10 + 14 ∙ 10
a14 = - 10 + 140
a14 = 130
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