JEE Mains · Maths · STD 11 - 8. sequence and series
The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by \(\frac{21}{2}\). Then the number of terms which are integers in the A.P. is :
- A \(4\)
- B \(10\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(\mathrm{a}_2+\mathrm{a}_4+\ldots+\mathrm{a}_{\mathrm{n}}=30\) ...(1) \(\mathrm{a}_1+\mathrm{a}_3+\ldots+\mathrm{a}_{\mathrm{n}-1}=24\) ...(2) \((1)-(2)\) \(\left(a_2-a_1\right)+\left(a_4-a_3\right) \ldots\left(a_n-a_{n-1}\right)=6\)…
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