Question

which term kf AP 38,33,28,23....is the first negative term? also find the sum of n term?

Answer 1

hope it helps
I forgot to mention r is a whole number so it can't be a fraction so r =9

Answer 2

9th term of AP will be the, First negative term of AP = -2

Sum of n terms = $\frac{n}{2} [81- 5n ]$.

Given:

38, 33, 28, 23.... is a Arithmetic sequence

To find:

First negative term

Solution:

Given series 38, 33, 28, 23....

Where, first term a = 38

common difference d = 33 - 38 = -5  

Here, we need to find first negative term

Let us assume that nth term is the first negative term

As we know nth term of AP, a$_{n}$ = a +(n-1)d  

Since  a$_{n}$ is negative term  a$_{n}$ < 0

⇒ a +(n-1)d  < 0  

⇒ 38+(n-1)(-5) < 0

⇒ 38 - 5n +5 < 0

⇒ 43 - 5n < 0

⇒ 43 < 5n  

⇒ n > 43/5

⇒ n > 8.6  

Since n is greater than 8.6

Therefore,  

at n = 9 the term will be the first negative term

⇒  a₉ = a +(n-1)d  

= 38 + (9-1)(-5)

= 38 + (8)(-5)  

= 38 - 40 = - 2

⇒ First negative term of AP = -2

As we know Sum of n term of AP = $\frac{n}{2} [2a+(n-1)d]$

= $\frac{n}{2} [2(38)+ (n-1)(-5) ]$  

= $\frac{n}{2} [76- 5n+5 ]$  

= $\frac{n}{2} [81- 5n ]$

9th term of AP will be the, First negative term of AP = -2

Sum of n terms = $\frac{n}{2} [81- 5n ]$.

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