Question

There are 4n+1 terms in a sequence of which first 2n+1 are in Arithmetic Progression and last 2n+1 are in Geometric Progression the common difference of Arithmetic Progression is 2 and the common ratio of geometric Progression is 1/2. The middle term of Arithmetic is equal to middle term of geometric progression.Let middle term of the sequence is Tm and Tm is the sum of geometric progression whose sum of two terms is (5/4)^2n amd ration of terms is 9/16

Answer 1

No of terms of the sequence-
A)9 B)17 C) 13 D)None of the above

Answer 2

2)Middle term of the given sequence is equal to
A)16/7 B)32/7 C)48/7 D)16/9
3)First term of the given sequence
(A)-8/7 B)-36/7 C)36/7 D48/7

Answer 3

4)Middle term of the given AP
A)6/7 B)10/7 C)78/7 D)11

Answer 4

5)Sum of the terms of AP
A)6/7 B)7 C)3 D)6

Answer 5

@hartnn @dan815 @ganeshie8 @Miracrown @goformit100 @Luigi0210 help

Answer 6

@ikram002p help

Answer 7

@Sheraz12345 hlp

Answer 8

is the sum of geometric progression whose sum of two terms is (5/4)^2n amd ration of terms is 9/16 ?

whose sum of two terms ??

Answer 9

@satellite73 hlp

Answer 10

yes

Answer 11

im still confused about this part
whose sum of two terms ( does it mean it has 2 terms in it ?)

Answer 12

let's see...
the first 2n+1 terms are in AP and the common difference is 2
so, if the first term would be just a
what would be the next term? @kanwal32

Answer 13

that means we have \(T_{n-1} ,T_{n} , T_{n+1}\) series such that its Arithmatic and Geometric at the same time

Answer 14

but for my doubt a series of 2n+1 can't have even term's
and you say its 2
mmm idk im confused with this
maybe it have 3 terms ?

Answer 15

first term is a
so the next term would be a + 2
and the next term would be a+2 + 2 = a+ 4
and the term 2n+1 would be
let me remind you the formula
a_final = a_initial + (n-1)*d
where n is the term number and d the common difference
so, let's write the last term of the AP
the idea is to use the formula for the n-th term
in opur case the last term is 2n+1

in the case of 2n+1 terms
we would have:

n first terms , ( n+1 )th term , n terms more
so, we need to find the a_n+1 term