JEE Mains · Maths · STD 11 - 8. sequence and series
Suppose \(a_1, a_2, 2, a_3, a_4\) be in an arithmeticogeometric progression. If the common ratio of the corresponding geometric progression is \(2\) and the sum of all \(5\) terms of the arithmetico-geometric progression is \(\frac{49}{2}\), then \(a_4\) is equal to \(...........\).
- A \(15\)
- B \(14\)
- C \(16\)
- D \(41\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
\(\frac{(a-2 d)}{4}, \frac{(a-d)}{2}, a, 2(a+d), 4(a+2 d)\) \(\left(\frac{1}{4}+\frac{1}{2}+1+6\right) \times 2+(-1+2+8) d=\frac{49}{2}\) \(\left(\frac{3}{4}+7\right)+9 d=\frac{49}{2}\) \(9 d=\frac{49}{2}-\frac{62}{4}=\frac{98-62}{4}=9\) \(d=1\) \(\Rightarrow a_4=4(a+2 d)\)…
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