determine k so that 2/3, k and 5/8k are the three consecutive terms of an AP which term of - Maths - Arithmetic Progressions

Question

determine k so that 2/3, k and 5/8k are the three consecutive
terms of an AP
which term of the progression 19, 91/5, 87/5 is the first
negative term
check if 50 is a term of an AP 4, 7, 10, 13, or not? if yes
find which term it is?

Lalit Mehra · Accepted Answer

Dear Student! 1 The given sequence of numbers $19, \frac{91}{5}, \frac{87}{5}, is an A P$ Here, $a = 19, d = \frac{91}{5} - 19 = \frac{91 - 95}{5} = - \frac{4}{5}$ Let nth term be the first negative term of the A P ${∴ a}_{n} < 0 \Rightarrow 19 + (n - 1) \times (- \frac{4}{5}) < 0 (∵ a_{n} = a + (n - 1) d) \Rightarrow (n - 1) (- \frac{4}{5}) < - 19 \Rightarrow n - 1 > \frac{19 \times 5}{4} \Rightarrow n > \frac{95}{4} + 1 = \frac{95 + 4}{4} = \frac{99}{4} = 24 75 \Rightarrow n > 24 75$ Thus, 25th term is the first negative term of the given A P 2 4, 7, 10, 13, is an A P Let 50 be the nth term of the given A P Here, a = 4 and d = 3 an = 50 $∴ 4 + (n - 1) \times 3 = 50 \Rightarrow 3 n - 3 = 50 - 4 = 46 \Rightarrow 3 n = 46 + 3 = 49 \Rightarrow n = \frac{49}{3} = 16 33, which is not an integer$ Thus, 50 is not a term of the given A P Cheers!

determine k so that 2/3, k and 5/8k are the three consecutive terms of an AP. which term of the progression 19, 91/5, 87/5 .... is the first negative term. check if 50 is a term of an AP 4, 7, 10, 13,.... or not? if yes find which term it is?

determine k so that 2/3, k and 5/8k are the three consecutive terms of an AP.

which term of the progression 19, 91/5, 87/5 .... is the first negative term.

check if 50 is a term of an AP 4, 7, 10, 13,.... or not? if yes find which term it is?