Question

ull n.P. Is (pn + qn), where p
and
find the common difference,
9 are constants,
9. The sums of n terms of two arithmetic progressions are in the ratio
5n+4: 9n + 6. Find the ratio of their 18th terms.
10. If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then
find the sum of the first (p + q) terms.
11. Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
b
-(q-r)+(r-p)+-(p-q)=0
р
a
a
Prove that
r
12. The ratio of the sums of m and n terms of an A.P. is m?: n?. Show that the ratio
of mth and nth term is (2m – 1): (2n – 1).
13. If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value
of m.
14. Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
a" +6"
is the A.M. between a and b, then find the value of n.​

Answer 1

Answer:

We are given the sum of n terms of an A.P. to be pn+qn

2

.

For n=1 in the given sum, we will get the first term and it is p+q.

For n=2 in the given sum, we get the sum of first and second term and it is 2p+4q.

Now the second term = the sum of first two term - first term=(2p+4q)−(p+q)=(p+3q).

The common difference of the A.P. is the difference between the first and second term and it is (p+3q)−(p+q)=2q.