The terms a1, a2, a3 (in that order) form an increasing arithmetic sequence whose sum is 18 . If a 1+1, a 2, a 3+2 form a geometric sequence (in that order), then sum of all possible values of a 1 is

Question

The terms a1, a2, a3 (in that order) form an increasing arithmetic sequence whose sum is 18 . If a 1+1, a 2, a 3+2 form a geometric sequence (in that order), then sum of all possible values of a 1 is (A) 2 (B) 11 (C) 13 (D) 9

Tardigrade Admin · Accepted Answer

a-d, a, a+d arrow A.P. 3 a =18 ∴ a =6 text Now 7- d , 6,8+ d arrow text G.P. ∴ 36=(7- d )(8+ d ) ∴ d =4 text or -5 text (rejected) ⇒ a 1=2 ⇒ S =2 .

Q. The terms $a_{1}, a_{2}, a_{3}$ (in that order) form an increasing arithmetic sequence whose sum is 18 . If $a_{1} + 1, a_{2}, a_{3} + 2$ form a geometric sequence (in that order), then sum of all possible values of $a_{1}$ is

2

11

13

9

$a - d, a, a + d \to$ A.P.
$3 a = 18$
$∴ a = 6$
$Now 7 - d, 6, 8 + d \to G.P.$
$∴ 36 = (7 - d) (8 + d)$
$∴ d = 4 or - 5 (rejected)$
$\Rightarrow a_{1} = 2 \Rightarrow S = 2.$

Q. The terms a1​,a2​,a3​ (in that order) form an increasing arithmetic sequence whose sum is 18 . If a1​+1,a2​,a3​+2 form a geometric sequence (in that order), then sum of all possible values of a1​ is

2

11

13

9

a−d,a,a+d→ A.P. 3a=18 ∴a=6 Now 7−d,6,8+d→ G.P. ∴36=(7−d)(8+d) ∴d=4 or −5 (rejected) ⇒a1​=2⇒S=2.

Q. The terms $a_{1}, a_{2}, a_{3}$ (in that order) form an increasing arithmetic sequence whose sum is 18 . If $a_{1} + 1, a_{2}, a_{3} + 2$ form a geometric sequence (in that order), then sum of all possible values of $a_{1}$ is

$a - d, a, a + d \to$ A.P.
$3 a = 18$
$∴ a = 6$
$Now 7 - d, 6, 8 + d \to G.P.$
$∴ 36 = (7 - d) (8 + d)$
$∴ d = 4 or - 5 (rejected)$
$\Rightarrow a_{1} = 2 \Rightarrow S = 2.$