Find the missing terms of the arithmetic sequence: 145, ___, ___, ___, 205 190, 175, 160 155, 165, 175 165, 185, 195 160, 175, 190
Answers
Given : arithmetic sequence: 145, ___, ___, ___, 205
To Find : missing terms of the arithmetic sequence:
190, 175, 160
155, 165, 175
165, 185, 195
160, 175, 190
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
arithmetic sequence: 145, ___, ___, ___, 205
1st term = 145
2nd , 3rd and 4th term are missing
5th term is 205
205 = 145 + ( 5 - 1) d
=> 60 = 4d
=> d = 15
2nd term = 145 + d = 145 + 15 = 160
3rd term = 145 + 2d = 145 + 2(15) = 175
4th term = 145 + 3d = 145 + 3(15) = 190
arithmetic sequence: 145, 160, 175,190, 205
missing terms of the arithmetic sequence: 160, 175, 190
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