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8. sequence and series — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS8. sequence and series1 Mark
MCQ
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
    $14$
  • ✓
    $16$
  • D
    $41$
✓

Answer

Correct option: C.
$16$
c
$\frac{(a-2 d)}{4}, \frac{(a-d)}{2}, a, 2(a+d), 4(a+2 d)$

$\left(\frac{1}{4}+\frac{1}{2}+1+6\right) \times 2+(-1+2+8) d=\frac{49}{2}$

$\left(\frac{3}{4}+7\right)+9 d=\frac{49}{2}$

$9 d=\frac{49}{2}-\frac{62}{4}=\frac{98-62}{4}=9$

$d=1$

$\Rightarrow a_4=4(a+2 d)$

$=16$

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