X times 3+6 when X equals four
2 answers:
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Answer:
The ratio of the first term to the common difference is 1 : 2
Step-by-step explanation:
The rule of the sum of the AP is
, where
a is the first number
d is the common difference
n is the position of the number
∵ = 4 ×
⇒ (1)
→ Find and
∵ In n = 10
∴
∴
∴ = 10a + 45d ⇒ (2)
∵ In n = 5
∴
∴
∴ = 5a + 10d ⇒ (3)
→ Substitute (2) and (3) in (1)
∵ 10a + 45d = 4[5a + 10d]
∴ 10a +45d = 20a + 40d
→ Subtract 40d from both sides
∴ 10a + 45d - 40d = 20a + 40d - 40d
∴ 10a + 5d = 20a
→ Subtract 10a from both sides
∴ 10a - 10a + 5d = 20a - 10a
∴ 5d = 10a
→ Divide both sides by 5
∴ d = 2a
→ That means d is twice a or a is half d
∴ a : d = 1 : 2
The ratio of the first term to the common difference is 1 : 2