JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\mathrm{T}_{\mathrm{r}}\) be the \(\mathrm{r}^{\text {th }}\) term of an A.P. If for some \(\mathrm{m}, \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}\), and \(20 \sum_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=13\), then \(5 \mathrm{~m} \sum_{\mathrm{r}=\mathrm{m}}^{2 \mathrm{~m}} \mathrm{~T}_{\mathrm{r}}\) is equal to
- A 98
- B 126
- C 142
- D 112
Answer & Solution
Correct Answer
(B) 126
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}, 20 \sum_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=13 \\ & \mathrm{~T}_{\mathrm{m}}=\mathrm{a}+(\mathrm{m}-1) \mathrm{d}=\frac{1}{25} \ldots \ldots .(1) \\ & \mathrm{T}_{25}=\mathrm{a}+24…
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