Question

Show that the sequence defined by an= 4n+5 is an AP.Also , find its common difference...also find the sum of 6 terms...

Answer 1

Answer:

an = 4n +5

Step-by-step explanation:

a1=4×1+5 (take n=1)

=9

a2=4 ×2 +5

=13

d=13-9 (a2-a1)

d=4

a6=4×6+5

=29

S6=n/2×{a+l}

=6/2×{9+29}

=3×38

=114

Answer - Common Difference=4

Sum of 6 terms=114

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Answer 2

The sum of 6 terms is 144 and common difference is 4

Step-by-step explanation:

Given : $a_n= 4n+5$

To find: The sum of 6 terms and common difference

Now

$a_1= 4\times 1+5= 9$

$a_2= 4\times 2+5=13$

$a_3= 4 \times 3+5= 17$

$a_4= 4\times 4+5 =21$

and so on

Therefore the A.P. is

9 , 13, 17, 21.......  

Therefore

$d= a_2-a_1= 13-9 = 4$

Similarly

$d= a_3-a_2= 17-13=4$

Therefore it is an A.P.

Now a is the first term d is the common difference n is the number of terms

Sum of n terms of A.P. is given by

$S_n=\dfrac{n}{2} (2a+(n-1)d)\\\\\Rightarrow S_6=\dfrac{6}{2}(2\times 9+(6-1)\times 4)=3(18+5\times 4) = 3(18+20)= 144$

Hence the sum of 6 terms is 144 and common difference is 4

#Learn more

Find the sum of the terms of A.P 2,6,10,14....,32.

brainly.in/question/67201