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  • Suppose <img alt="\mathrm{a}_1, \mathrm{a}_2, 2, \mathrm{a}_3, \mathrm{a}_4" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Ba%7D_1%2C%20%5Cmathrm%7Ba%7D_2%2C%202%2C%20%5Cmathrm%7B

Suppose \mathrm{a}_1, \mathrm{a}_2, 2, \mathrm{a}_3, \mathrm{a}_4 be in an arithemetico-geometric progression. If the common ratio of the corresponding geometric progression in 2 and the sum of all 5 terms of the arithmetico-geometric progression is \frac{49}{2}, then a_4 is equal to_________.

Option: 1

16


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \frac{(a-2 d)}{4}, \frac{(a-d)}{2}, a, 2(a+d), 4(a+2 d) \\ & a=2 \\ & \left(\frac{1}{4}+\frac{1}{2}+1+6\right) \times 2+(-1+2+8) d=\frac{49}{2} \\ & 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) \\ & =16 \end{aligned}

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