Now that we have d, let’s solve first the using the general equation for arithmetic sequence. You can use either the a3 or a13.
For this one, I will be showing you the process using the a3. an = a1 + (n-1) d, a3 = 63, n=3, d=-3a3 = a1 +(3-1) (-3)63 = a1 - 6a1 = 63 + 6 = 69
I'll give you some tips on how to solve for harmonic sequence. The first thing that you need to do is to get the reciprocal and apply the ways of solving an arithmetic sequence.
Thank you for that explanation and examples Ica. This time, we will be discussing about the harmonic sequence.
Harmonic sequence is a special type of sequence that is related to the arithmetic sequence wherein the reciprocals of its sequence of numbers can form an arithmetic sequence.
To solve it easily, get first their reciprocals, so we have, 2, -1, _____, -7, -10, _____. Using the knowledge that we learn from the arithmetic sequence, we can get the difference by subtracting 2 consecutive terms and by so our d = -1 - 2 =-3.
Let's us have some examples for our students to understand what you are saying Ric.
For example, we are task to find the missing terms of the following harmonic sequence: 1/2, -1, _____, -1/7, -1/10, _______.
After solving the common difference, you can either use the formula for arithmetic sequence or just add directly to the previous terms like -1 + (-3) = -4 and -10 + (-3) = -13.
In this given problem, the missing numbers are -1/4 and -1/13. For more exercise and problems, please ask it from Sir Roy and please always do listen to him during your face to face class.
Take note that after solving the missing numbers, in harmonic sequence, you must always get the reciprocal of your answer to make it part of the sequence.