Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make bags that have
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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:
1) 11
2) 2
3)
4)
5) -2
6)
Step-by-step explanation:
1) 2 + 3
-
=(2 × 2 )+ (3 × 4
) - 5
= 4 + 12
- 5
= 11
2) 4 -2
+
= (4 × 2) - (2 × 7
) + 8
= 8 - 14
+8
= 2
3) 5 - 3
= 5× - 3×
+ 4×
+ 2×
=
=
4)
=
=
5)
=
= -2
6)
=
= 2× - 2×
-
=
=
Hope the working out is clear and will help you. :)