Sequences and Series
Calculate the greatest and least values of the functionf(x)=x8+2x6−4x4+8x2+16x4
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The pth,qthand rthterms of an A.P. are a, b, c, respectively. Show that (q−r)a+(r−p)b+(p−q)c=0.
If A.M. and GM. of two positive numbers a and b are 10 and 8, respectively find the numbers.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
If the 3rd and the 9thterms of an AP are 4 and −8 respectively, which term of this AP is zero?
Find the sum of the odd numbers between 0 and 50.
Determine the AP whose third term is 16 and the 7thterm exceeds the 5thterm by 12.
The sums of n terms of two arithmetic progressions are in the ratio 5n+4:9n+6. Find the ratio of their 18thterms.
Find the sum of first 22 terms of an AP in which d=l and 22nd term is 149.