Question

Sum of the terms of an arithmetic sequence having 5 terms is 105

a) What is the third term of the sequence?

b) What is the sum of the first term and the fifth term?

answer and explanation​

Answer 1

Answer:

Series is in AP

1  

st

 and 5  

th

 term sum=26

Let a is the first term and d is the common difference.

a  

r

​

=a+(r−1)d

a+a+(5−1)d=26

2a+4d=26

a+2d=13−(i)

2  

nd

 and 4  

th

 term product =160

a=13−2d

(a+d)(a+3d)=160−(ii)

Putting value of a from (i) in (ii)

(13−2d+d)(13−2d+3d)=160

(13−d)(13+d)=160

169−d  

2

=160

d  

2

=9d=3

Putting value of d in (i)

a=13−2(3)

a=13−6

a=7

Sum of first 6 terms

=  

2

n

​

(2a+(n−1)d)

=  

2

6

​

(2(7)+(6−1)(3))

=3(14+5(3))

=3(14+15)

=3(29)=87

Sum of first 6 terms=87.

Step-by-step explanation:

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