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Question
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
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Solution
Given that,
`\implies` an = 5 + 6n
We have,
`\implies` a1 = 5 + 6(1) = 11
`\implies` a2 = 5 + 6(2) = 17
So, a = 11, d = 6
Sum of first 25 terms = `n/2(2a + (n - 1)d)`
= `25/2[2(11) + (25 - 1)6]`
= `25/2[22 + 144]`
= `25/2[166]`
= 2075
Now, a20 = a + 19d
= 11 + 19(6)
= 125
`\implies` a45 = a + 19d
= 11 + 44(6)
= 275
Required ratio = `a_20/a_45`
= `125/275`
= `5/11`
Ratio is 5:11.
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