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The common difference ‘d’ of the A.P. in which $T_7 = 9$ and $T_1 T_2 T_7$ is least, is
Option: 1
16

Option: 2
43955

Option: 3
1.65

Option: 4
none

Answers (1)

best_answer

General term of an A.P. -

$T_{n}= a+\left ( n-1 \right )d$

- wherein

$a\rightarrow$ First term

$n\rightarrow$ number of term

$d\rightarrow$ common difference

$a + 6d = 9$

$T_1 T_2 T_7 = a(a + d) (a + 6d)$

$= 9a (a + d) = 9( 9-6d) (9-5d)$

$T_7 = a+ 6d = 9$

Let $A =T_1 T_2 T_7$

$\frac{dA }{d(d)}=9[-45-54+60d]=0$

$60 d = 99$

$d =33/20$

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