The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is

Question

The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is (A) - 42 (B) 66 (C) - 21 (D) 34

Tardigrade Admin · Accepted Answer

a ; a+9 ; a+18 ; ldots ldots. Now, a1, a3 and a8 in G.P. i.e. a, a+18 and a+63 in G.P. ∴(a+18)2=a(a+63)=a2+63 a ⇒ a=12 ; d=9 So, a7=a+6 d=12+54=66.

Q. The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is

- 42

66

- 21

34

$a; a + 9; a + 18; \dots\dots$ .
Now, $a_{1}, a_{3}$ and $a_{8}$ in G.P. i.e. $a, a + 18$ and $a + 63$ in G.P.
$∴ (a + 18)^{2} = a (a + 63) = a^{2} + 63 a \Rightarrow a = 12; d = 9$
So, $a_{7} = a + 6 d = 12 + 54 = 66$ .

Q. The first, third and eighth terms of an arithmetic sequence with common difference 9 (taken in that order) are in geometric progression. The seventh term of arithmetic sequence is

- 42

66

- 21

34

a;a+9;a+18;……. Now, a1​,a3​ and a8​ in G.P. i.e. a,a+18 and a+63 in G.P. ∴(a+18)2=a(a+63)=a2+63a⇒a=12;d=9 So, a7​=a+6d=12+54=66.

$a; a + 9; a + 18; \dots\dots$ .
Now, $a_{1}, a_{3}$ and $a_{8}$ in G.P. i.e. $a, a + 18$ and $a + 63$ in G.P.
$∴ (a + 18)^{2} = a (a + 63) = a^{2} + 63 a \Rightarrow a = 12; d = 9$
So, $a_{7} = a + 6 d = 12 + 54 = 66$ .