The ratio of the 11th term of an AP to the 8th term is 23 find the ratio of the 5th term to 21st isn't the ratio of their sums 5:9.

Let the first term and common difference of an A.P. is a and d respectively.

We know that,

Now, we are asked to find . So,

Substitute value of a from equation (3), we get,

Sum of first 5 term  and first 21 terms of an A.P. be as,

Substitute value of a from equation (3), we get,

Hence, the ratio of fifth and 21st term is -3 : 1 and the ratio of sum of first 5 terms and first 21 terms is 5 : 9

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