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2 answers:
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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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Answer:
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
Step-by-step explanation:
The base of the quadratic function is
We can transform this function to look narrower or wider.
Looking narrower is termed a stretch.
This happens when a>1
Looking wider is termed a compression.
This happens when 0<a<1
We can also
+h moves the parent graph to the left by h units
-h moves the parent graph to the left by h units.
+ k moves the parent function up by k units
- k moves the parent function down by k units.
The change that occurs to
given
is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up
Therefore the last choice is the correct answer.