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Question 13. If the sum of n terms of an A.P. is \( 3n^2+5n\) and its mth term is 164, find the value of m.


Question 14. Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Question 15. If \( \frac{a^n+b^n}{a^{n-1}+b^{n-1}} \) is the A.M. between a and b, then find the value of n.


Question 16. Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7th and (m – 1)th numbers is 5 : 9. Find the value of m.

Question 17. A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?


Question 18. The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120° , find the number of the sides of the polygon.


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