CBSE Class 11-science Answered
7th sum
![question image](https://images.topperlearning.com/topper/new-ate/5125284139403267rps20190202183545.jpg)
Asked by lovemaan5500 | 02 Feb, 2019, 20:26: PM
Let a be the first term and d be the common difference of an AP.
tp = a + (p - 1)d
tq = a + (q - 1)d
tr = a + (r - 1)d
According to the question terms are in GP
[a + (q - 1)d]2 = [a + (p - 1)d][a + (r - 1)d]
simplifying this we get
a =
and r = ![begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style](https://images.topperlearning.com/topper/tinymce/cache/6d3b500344bf876f0c6c5ad2267bb143.png)
![begin mathsize 16px style fraction numerator negative left parenthesis straight q squared minus 2 straight q minus pr plus straight p plus straight r right parenthesis straight d over denominator 2 straight q minus straight r minus straight p end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/0887225dda0e1af6fa55e8e8442da128.png)
![begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style](https://images.topperlearning.com/topper/tinymce/cache/6d3b500344bf876f0c6c5ad2267bb143.png)
Solving r = ![begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style](https://images.topperlearning.com/topper/tinymce/cache/6d3b500344bf876f0c6c5ad2267bb143.png)
![begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style](https://images.topperlearning.com/topper/tinymce/cache/6d3b500344bf876f0c6c5ad2267bb143.png)
we get r = ![begin mathsize 16px style fraction numerator straight q minus straight r over denominator straight p minus straight q end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/876a528b80190a9084fe5705c44e8c8b.png)
![begin mathsize 16px style fraction numerator straight q minus straight r over denominator straight p minus straight q end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/876a528b80190a9084fe5705c44e8c8b.png)
Answered by Sneha shidid | 04 Feb, 2019, 13:04: PM
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