Question

the number of terms of the series 26+24+22+...such that the sum is 182 is​

Answer 1

Answer:

14

Step-by-step explanation:

Sn=n÷2(2a+(n-1)d)

182=n÷2(2(26)+(n-1)(-2)

364=n(52-2n+2)

364=54n-2n²

2n²-54n+364=0

n²-27n+182=0

n²-14n-13n+182=0

n(n-14)-13(n-14)=0

(n-13)(n-14)=0

Answer 2

The number of terms can be 13 and 14.

Step-by-step explanation:

Since we have given that

$26+24+22.......................=182$

Here, a = 26

d = common difference = -2

So, it becomes,

$S_n=\dfrac{n}{2}(2a+(n-1)d)\\\\182=\dfrac{n}{2}(2\times 26+(n-1)(-2))\\\\182\times 2=n(52-2n+2)\\\\364=n(54-2n)\\\\364=54n-2n^2\\\\2n^2-54n+364=0\\\\n^2-27n+182=0\\\\n^2-13n-14n+182=0\\\\n(n-13)-14(n-13)=0\\\\n=13,14$

Hence, the number of terms can be 13 and 14.

# learn more:

If the sum of a number and it's square is 182 ,then the Number is

A . 13

B . 26

C . 28

D . 15​