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Question
Verify that the following is an AP, and then write its next three terms.
`0, 1/4, 1/2, 3/4, ...`
Solution
Here,
a1 = 0
a2 = `1/4`
a3 =`1/2`
a4 = `3/4`
a2 – a1 = `1/4 - 0 = 1/4`
a3 – a2 = `1/2 - 1/4 = 1/4`
a4 – a3 = `3/4 - 1/2 = 1/4`
Since, difference of successive terms are equal,
Hence, `0, 1/4, 1/2, 3/4,...` is an AP with common difference `1/4`
Therefore, the next three term will be,
a5 = a1 + 4d
= `0 + 4(1/4)`
= 1
a6 = a1 + 5d
= `0 + 5(1/4)`
= `5/4`
a7 = a1 + 6d
= `0 + 6/4`
= `3/2`
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