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Question
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
12, 2, −8, −18, ...
Solution
In the given problem, we are given various sequences.
We need to find out that the given sequences are an A.P or not and then find its common difference (d)
12, 2, −8, −18, ...
Here,
First term (a) = 12
`a_1 = 2`
`a_2 = -8`
Now, for the given to sequence to be an A.P,
Common difference (d) = `a_1 - a = a_2 - a_1`
Here
`a_1 - a = 2 - 12`
= - 10
Also
`a_2 - a = -8 - 2`
= - 10
Since `a_1 - a = a_2 - a_1`
Hence, the given sequence is an A.P with the common difference d = -10
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Case Study Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body.
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- Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished?
- Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.
If the terms 10, a, 40 are in A.P., then find the value of a.
