Question

If the ratio of the sum of the first n terms of two A.Ps is (7n+1):(4n+27) , then find the ratio of their mth terms?

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Answer 1

1. Question⇒    If the ratio of the sum of the first n terms of two A.Ps is (7n+1):(4n+27) , then find the ratio of their mth terms?

Step-by-step explanation:

• [n2(2a1+(n−1)d1)][n2(2a2+(n−1)d2)]=7n+14n+27
• Cancelling common terms on the left hand side,
• (2a1+(n−1)d1)(2a2+(n−1)d2)=7n+14n+27
• Taking 2 common on both sides,
• ∴(a1+(n−1)2d1)(a2+(n−1)2d2)=7n+124n+272
• ∴(a1+(n−1)2d1)(a2+(n−1)2d2)=7n+14n+27...(equation1)
• Now we have to find the ratio of 9th term, in mathematical terms we have to find,
• (a1+8d1)(a2+8d2).....(equation2)
• Look closely at equation 2 and equation number 1. In equation number 1, if
• (n−1)2=8
• ∴n−1=16
• ∴n=17
• Putting n=17 in equation number 1 we get,
• ∴(a1+8d1)(a2+8d2)=7∗17+14∗17+27
• ∴(a1+8d1)(a2+8d2)=12095
• Simplifying further we get,

• ∴(a1+8d1)(a2+8d2)=24/19    
• 24/19 Answer