f five times a number is subtracted from twelve times a number, the result is seven less than twice the number. Find the number
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The sum of the first four terms of the sequence is 22.
In this question,
The formula of sum of linear sequence is
The sum of the first ten terms of a linear sequence is 145
⇒
⇒ 145 = 5 (2a+9d)
⇒
⇒ 29 = 2a + 9d ------- (1)
The sum of the next ten term is 445, so the sum of first twenty terms is
⇒ 145 + 445
⇒
⇒ 590 = 10 (2a + 19d)
⇒
⇒ 59 = 2a + 19d -------- (2)
Now subtract (2) from (1),
⇒ 30 = 10d
⇒ d =
⇒ d = 3
Substitute d in (1), we get
⇒ 29 = 2a + 9(3)
⇒ 29 = 2a + 27
⇒ 29 - 27 = 2a
⇒ 2 = 2a
⇒ a =
⇒ a = 1
Thus, sum of first four terms is
⇒
⇒
⇒ S₄ = 2(2+9)
⇒ S₄ = 2(11)
⇒ S₄ = 22.
Hence we can conclude that the sum of the first four terms of the sequence is 22.
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Check the picture below.
so... if Julia folded the paper, in a way that P was on top of Q, that means the crease is running through the half-way point or midpoint, that means that, if the segment PQ is 2.4, the segments on either side of the crease, PS and QS are both two equal halves.
so... if Julia folded the paper, in a way that P was on top of Q, that means the crease is running through the half-way point or midpoint, that means that, if the segment PQ is 2.4, the segments on either side of the crease, PS and QS are both two equal halves.