If a 1 , … , a 5 are in H.P., find a 1 a 2 + a 2 a 3 + a 3 a 4 + a 4 a 5 .

Start Free Mock LoginAlready registered? Login here

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesH.P.Medium2 minQB

MathematicsMediumsingle choice

If $a_{1}, \dots, a_{5}$ are in H.P., find $a_{1} a_{2} + a_{2} a_{3} + a_{3} a_{4} + a_{4} a_{5}$ .

Options:

Answer:

Solution:

For successive harmonic terms $x, y, z, (x + z) y = 2 x z$ . Apply this at indices $(1, 2, 3)$ and $(3, 4, 5)$ : the sum is $2 a_{3} (a_{1} + a_{5})$ . Applying the same identity to $(1, 3, 5)$ gives $a_{3} (a_{1} + a_{5}) = 2 a_{1} a_{5}$ , hence the result is $4 a_{1} a_{5}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:H.P.

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...