Question

Write the sum using summation notation, assuming the suggested pattern continues.

-4 + 5 + 14 + 23 + ... + 131

Answer 1

Don't you think it's follows a pattern
Every successive term is 9 more than previous term

Answer 2

So it's an AP series

Answer 3

Can you find total number of terms in this series.

Answer 4

i dont know how

Answer 5

wait is it 15?

Answer 6

You know the formula to find last term of AP series

Answer 7

no i dont

Answer 8

The formula is
Last term= first term + (n-1)d
Where n=no. Of term and d=difference between two successive term

Answer 9

is n 15

Answer 10

Let's check by formula
135=-4 +(n-1)9
can you understand this

Answer 11

wait why 135 isnt it 131

Answer 12

Just respective values are plugged

Answer 13

Yes right

Answer 14

131=-4 +(n-1)9

Answer 15

Can you solve it for n

Answer 16

131=-4+9n-9
131=9n-13
9n=144
n=16

Answer 17

Right

Answer 18

Now you know the summation of AP series?

Answer 19

no

Answer 20

wait

Answer 21

is it

Answer 22

summation of the (-4+9n) from n equals zero to fifteen

Answer 23

Sorry that is (n/2)[2a+(n-1)d]
OR (n/2)sum of first and last term

Answer 24

You can do now

Answer 25

what?

Answer 26

Sum =16/2(-4+131)
=8(128)= 1024