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find the common difference of an ap whose first term is 100 and sum of whose first 6 terms is 5 times the sum of next 6 termsans a
find the middle term of the ap 1 8 15505ans middle termsa n-1d 505a n-17 505n - 1 5047n 73there4 37th term is middle terma37 a
if 1x2 1x3 1x5 are in ap find xans 1x21x3 1x5 are in ap find x1x3 - 1x2 1x5-1x3gt 1x2 5x6 2 x2 8x 15gt on solving we get x
if the pth term of an ap is q and the qth term is p pt its nth term is pq-nans apqap qaq pan a p-1 d qa q-1 d pdp - q q - p
write the next two terms radic12 radic27 radic48 radic75ans next two terms radic108 radic147 ap is 2 radic3 3 radic3 4 radic3 5
find the sum of ab a-b a-3b to 22 termsans a b a - b a - 3b up to 22 terms d a - b - a - b 2bs22 222 2ab21-2b112a 2b - 42b 22a - 440b
if the following terms form a ap find the common difference amp write the next3 terms3 3 radic2 32radic2 33radic2ans d radic2 next three
find the sum of 1 - 1n 1 - 2n 1 - 3n upto n termsans 1 - 1n 1 - 2n - upto n terms rarr11n terms - 1n 2n n termsn -sn
balls are arranged in rows to form an equilateral triangle the first row consists of one ball the second two balls and so on if 669 more
if the roots of the equation b-cx2 c-ax a-b 0 are equal show that a b c are in apans refer sum no12 of qeif b-cx2 c-ax a-bx have equal
prove that am n am - n 2amans a m n a1 m n - 1 da m-n a1 m - n -1 dam a1 m-1 dadd 1 amp 2a mn a m-n a1mn-1 d
raghav buys a shop for rs120000he pays half the balance of the amount in cash and agrees to pay the balance in 12 annual instalments of rs5000 each
find the value of x if 2x 1 x2 x 1 3x2 - 3x 3 are consecutive terms of an apans a2 -a1 a3 -a2rarr x2 x 1-2x - 1 3x2 - 3x 3-
find the sum of all 3 digit numbers which leave remainder 3 when divided by 5ans 103 108998 a n-1d998rarr103 n-15998rarrn180s180
a man arranges to pay a debt of rs3600 in 40 monthly instalments which are in a ap when 30 instalments are paid he dies leaving one third of the debt
find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or
if the pth qth amp rth term of an ap is x y and z respectively show that xq-r yr-p zp-q 0ans pth term rarr x a p-1 dqth term rarr y
find the 20th term from the end of the ap 3 8 13253ans 3 8 13 253last term 253 a20 from end l - n-1d253 - 20-1 5253 - 95
arithmetic progressions one of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a
if the roots of the equation a-bx2 b-c x c - a 0 are equal prove that 2abcans a-bx2 b-c x c - a 0tp 2a b cb2 - 4ac 0b-c2 - 4a-b c -
a pole has to be erected at a point on the boundary of a circular park of diameter 13m in such a way that the differences of its distances from two
a teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over when he increased
the positive value of k for which x2 kx 64 0 amp x2 - 8x k 0 will have real roots ans x2 kx 64 0rarr b2 -4ac gt 0k2 - 256 gt 0k gt 16 or k
the hypotenuse of a right triangle is 20m if the difference between the length of the other sides is 4m find the sidesans apqx2 y2 202 x2 y2
a lotus is 2m above the water in a pond due to wind the lotus slides on the side and only the stem completely submerges in the water at a distance of