For the AP : $\frac{1}{4}, \frac{- 1}{4}, \frac{- 3}{4}, \frac{- 5}{4} \dots \dots$ , write the first term $a$ and the common difference $d$ . And find the $7^{th}$ term.

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Solution

Here, $a = \frac{1}{4}; d = \frac{- 1}{4} - \frac{1}{4} = \frac{- 1}{2}$
Remember that we can find $d$ using any two consecutive terms, once we know that the numbers are in AP.
The seventh term would be $\frac{- 5}{4} - \frac{1}{2} - \frac{1}{2} - \frac{1}{2} = \frac{- 11}{4}$

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For the AP : 14,−14,−34,−54……, write the first term a and the common difference d. And find the 7th term.

Here, a=14;d=−14−14=−12 Remember that we can find d using any two consecutive terms, once we know that the numbers are in AP. The seventh term would be −54−12−12−12=−114

For the AP : $\frac{1}{4}, \frac{- 1}{4}, \frac{- 3}{4}, \frac{- 5}{4} \dots \dots$ , write the first term $a$ and the common difference $d$ . And find the $7^{th}$ term.

Here, $a = \frac{1}{4}; d = \frac{- 1}{4} - \frac{1}{4} = \frac{- 1}{2}$
Remember that we can find $d$ using any two consecutive terms, once we know that the numbers are in AP.
The seventh term would be $\frac{- 5}{4} - \frac{1}{2} - \frac{1}{2} - \frac{1}{2} = \frac{- 11}{4}$