If 2, h_1, h_2,....., h_20, 6 are in harmonic progression and 2, a_1, a_2,...., a_20, 6 are in arithmetic progression, then the value of a_3h_18 is…

Question

If 2, h_1, h_2,....., h_20, 6 are in harmonic progression and 2, a_1, a_2,...., a_20, 6 are in arithmetic progression, then the value of a_3h_18 is equal to

MARKS Content Team · Accepted Answer

Correct answer: (B) 12. 1/2,1/h_1,1/h_2,....,1/h_20,1/6 are in A.P. ⇒1/6=1/2+21d⇒1/6-1/221=d ⇒d=-1/63 ⇒1/h_18=1/2+18d=1/2+182-1/637=1/2-2/7 1/h_18=3/14⇒h_18=14/3 Also, 2,a_1,a_2,.....,a_20,6 are in A.P. ⇒6=2+21D⇒D=4/21 ⇒a_3=2+3D=2+3×4/217=18/7 ⇒a_3h_18=186/7×142/3=12

If $2, h_{1}, h_{2}, . . . . ., h_{20}, 6$ are in harmonic progression and $2, a_{1}, a_{2}, . . . ., a_{20}, 6$ are in arithmetic progression, then the value of $a_{3} h_{18}$ is equal to

Solution

More Sequences and Series Questions

If 2, h1, h2,....., h20, 6 are in harmonic progression and 2, a1, a2,...., a20, 6 are in arithmetic progression, then the value of a3h18 is equal to

Solution

More Sequences and Series Questions

If $2, h_{1}, h_{2}, . . . . ., h_{20}, 6$ are in harmonic progression and $2, a_{1}, a_{2}, . . . ., a_{20}, 6$ are in arithmetic progression, then the value of $a_{3} h_{18}$ is equal to