MCQ
The common difference of the $A.P$ whose $S_n= 3n_2+ 7n$ is :
- A$5$
- B$1$
- C$2$
- ✓$6$
✓
Answer
Correct option: D.
$6$
Given : $S_n=3 n_2+7 n$
Putting $n = 1, 2, 3$ we get
$ S=a=3 \times(1)^2+7 \times 1=3+7=10 $
$ S_2=3 \times(2)^2+7 \times 2=12+14=26 $
$ S_3=3 \times(3)^3+7 \times 3=27+21=48$
Now, $a_2={S}_2-{S}_1=26-10=16$
$\therefore$ Common difference $(d)=a_2-a=16-10=6$
Putting $n = 1, 2, 3$ we get
$ S=a=3 \times(1)^2+7 \times 1=3+7=10 $
$ S_2=3 \times(2)^2+7 \times 2=12+14=26 $
$ S_3=3 \times(3)^3+7 \times 3=27+21=48$
Now, $a_2={S}_2-{S}_1=26-10=16$
$\therefore$ Common difference $(d)=a_2-a=16-10=6$
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