Question

Which of the following summations represent the series shown? Check all that apply.

11 + 17 + 23 + 29

Answer 1

SOLUTION

TO DETERMINE

Summation form that represent the series

11 + 17 + 23 + 29

EVALUATION

Here the given series is

11 + 17 + 23 + 29

It is an arithmetic series

First term = 11

Common Difference = 17 - 11 = 6

Now every term can be rewritten as below

11 = 5 + 6

17 = 11 + 6 = ( 2 × 6 ) + 5

23 = 17 + 6 = ( 3 × 6 ) + 5

29 = 23 + 6 = ( 4 × 6 ) + 5

Therefore

11 + 17 + 23 + 29

$= \displaystyle \sum\limits_{n=1}^{4} \: ( \: 6n + 5 \: )$

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Answer 2

Answer: This is an A.P.

Step-by-step explanation:

11+17+23+29 represents the sum of arithemetic  series 11, 17, 23 and 29

here,

First term(a)=11

common difference(d)=17-11

d=6

number of terms(n)=4

hence,

sum of terms in AP=n/2[2a+(n-1)d]

=4/2[(2×11)+(4-1)6]

=80