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Calculus/Sequence and Series
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Question
The Common difference of an Arithmetic progression is 2 and the common ratio of a geometric progression is 3. corresponding terms of the A.P and the G.P are added to form a new sequence. If the first term of this sequence is 8 and the third is 52. then find
A The first term of the A.P
B The first term of the G.p
The first terms of the AP is A and the GP is G.
This means A + G = 8.
The 2rd term is two terms away from the first term.
For the AP, it would be A + 2(2) = A + 4.
For the GP, it would be (G)3² = 9G.
It is known that A+4 + 9G = 52, so subtract 4 from both sides.
This gives A + 9G = 48.
This gives us two equation, two unknowns.
They are A + G = 8 and A + 9G = 48.
The 1st can be changed, by subtracting G from both sides,
to A = 8 - G. This can be put in the second. G can be found,
and then A is 8-G.
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| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |
| Comment | Thank you very much indeed I presumed that some terms of AP and GP were inserted in the sequence not added. That made it complicated. Cordially Michael | ||
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