AP -I

[maihuna]

The number of terms in an AP is even; the sum of the odd terms is 24, of the even terms 30, and the last term exceeds the first by 10.5; find the number of terms.

4
8
10
12
14

[maihuna]

There are two sets of numbers each consisting of 3 terms and sum of each set is 15. The common difference of the first is greater by 1 than the common difference of the second, and the product of first set is to the product of the second set as 7/8, what are the numbers.

[tohellandback]

You have already posted your 2nd question in some other thread.
Answer to your 1st question:
sum of odd terms=24
sum of even terms=30

let there be n terms



sum of odd terms:
the first term is a, last term is "last term of the series-common difference" i.e a+10.5-d
n/4(a+a+10.5-d)=24
n(2a+10.5-d)=96------------1

sum of even terms:
1st term is a+d, last term is a+10.5
n/4(a+d+a+10.5)=30
n(2a+10.5+d)=120----------2
subtract 1 from 2

2nd=24
nd=12
d=12/n--------------3
also given that

a+(n-1)d= a+10.5, where d is the common difference
d=10.5/(n-1)

d=10.5/n-1=12/n
10.5n=12n-12
1.5n=12
n=8

Answer B