Question

→Question 1 - If the sum of the first n terms of two APs is ( 3n+8 ) : ( 7n+15 ) . find the ratio of their 12th terms..

→Question 2 - The sum of first m terms of an AP is ( 4m² - m ). if its nth term is 107, find the value of n. Also , find the 21st term of this AP.

♦ Chapter - Arithmetic Progression

Solve both questions with explanation...
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Answer 1

Step-by-step explanation:

1]For 1st AP

Let first term be a common difference be d

sum of n terms sn=2n(2a+(n−1)d)

nth term an=a(n−1)d

Similarly for 2nd AP

Let first term =A common difference be D

Sn=2n(2A+(n−1)D) & nth term =An=A+(n−1)D

We need ratio of 12th term

i.e., A12ofsecondAPa12offirstAP

=A+(12−1)Da+(12−1)d

=a+11Da+11d

It is given that

Sumofntermsof2ndAPSumofntermsof1stAP=7n+153n+8

∴

2A+(n−1)D2a+(n−1)d=7n+153n+8 ………….(1)

2(A+(2n−1)D)2(a+(2n−1)d)=7n+153n+8 ………………(1)

we need to find A+11Da+11d

Hence 2n−1=11

n−1=22

n=23

Putting n=23 in (1)

A+(223−1)Da+(223−1)d=7×23+153×23+18

∴A+11Da+11d=167

Hence ratio of their 

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