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13. Given,

a₁=a₂=2.

a_n=a_{n – 1} – 1

Putting n=3,4,5.

a₃=a_{3 – 1} – 1=a_{3 – 1} – 1=a₂ – 1=2 – 1=1

a₄=a_{4 – 1} – 1=a₃ – 1=1 – 1=0

a₅=a_{5 – 1} – 1=a₄ – 1=0 – 1= –1 .

Hence the first five forms of the sequence are 2,2,1,0, –1.

And the series is 2+2+1+0+ (–1)+ ….

Candidates wishing to pursue the BSc course at NCAAS are required to select a specialisation based on their interest and career aim. The specialisations on offer that the candidates can choose from are:

• BSc in Aeronautical Science
• BSc in Aircraft Maintenance Science

BSc at NCAAS is a three year course and candidates who qualify the admissio process set for the course can pay the course fee to secure their seat in the programme. 

The following steps will help to identify the Adjectives:

1. Identify the Words that Describe Noun or Pronouns
2. Pay attention to the Position of the Adjectives
3. Ask questions about noun and pronoun to know the details
4. Pay Attention to Comparative and Superlative Forms
5. Pay Attention to Suffixes

The total tuition fee for BTech under Convenor Quota is INR 3.23 lakh. The total tuition fee for candidates seeking admission in BTech under Management Quota ranges between INR 3.24 lakh and INR 6.40 lakh. The fee is calculated considering the tuition fee per annum. Candidates have to pay the course fee at the time of admission to confirm their seat. 

12. Given, a₁= –1,

$a_n=\frac{a_{n-1}}{n},n\ge 2$

Putting n=2,3,4,5 we get,

$a_2=\frac{a_{2-1}}{2}=\frac{a_1}{2}=-\frac{1}{2}$

$a_3=\frac{a_{3-1}}{3}=\frac{a_2}{3}=\frac{-1/2}{3}=-\frac{1}{6}$

$a_4=\frac{a_{4-1}}{4}=\frac{a_3}{4}=\frac{-1/6}{4}=-\frac{1}{24}.$

$a_5=\frac{a_{5-1}}{5}=\frac{a_4}{5}=\frac{-1/24}{5}=-\frac{1}{120}$ .

So the first five terms of the sequence are –1, $-\frac{1}{2},-\frac{1}{6},-\frac{1}{24}$ and $-\frac{1}{120}$ .

And the series is $(-1)+\left(-\frac{1}{2}\right)+\left(-\frac{1}{6}\right)+\left(-\frac{1}{24}\right)+\left(-\frac{1}{120}\right)+\dots$ .

11. Given, a₁=3

a_n=3a_{n – 1}.+2  "n>1.

Putting n=2,3,4,5 we get,

a₂=3a_{2 – 1}+2=3a₁+2=3 * 3+2=9+2=11

a₃=3a_{3 – 1}+2=3a₂+2=3 * 11+2=33+2=35

a₄=3a_{4 – 1}+2=3a₃+2=3 * 35+2=105+2=107.

a₅=3a_{5 – 1}+2=3a₄+2=3 * 107+2=321+2=323.

Hence, the first five terms of the sequence are 3,11,35,107,323.

And the series is 3+11+35+107+323+ …

The Adjetives are of following types:

No, candidates wishing to apply to the courses at NCAAS are not required to pay an application fee to register for their desired course. Candidates are required to pay the course fee only. Once the course fee has been paid, candidates can continue to attend the regular classes. 

10.$a_n=\frac{x(x-2)}{x+3}$ .

Put n=20,

$a_{20}=\frac{20(20-2)}{20+3}=\frac{20\times 18}{23}=\frac{360}{23}$

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Raghu Engineering College considers Andhra Pradesh EAPCET scores for admission to BTech course. Students must score equal or more than the cutoff for admission. In 2023, CSE was the most competitive specialisation with Andhra Pradesh EAPCET cutoff of 9229. Below is the closing rank for Andhra Pradesh EAPCET of last three-years:

PES University offers PharmD as a 6 year course with an annual intake of 30 students. The University offers the respective course with a total tuition fees worth INR 16.8 Lakh. Admission to PharmD is offered on then basis of valid scores of KCET. Candidates must visit the official website to learn more about the eligibility criteria for the admission to PharmD. 

9. a_n= ( –1)^{n – 1} .n³.

Put n=9 we get,

a_q= (–1)^{9 – 1}.9³= (–1)⁸. 729=729.

You can enroll in PCE's B.Tech programs through management quota directly, in addition to the regular routes using the JEE Main and REAP counselling methods.

Candidates can join Poornima College of Engineering directly.
Eligibility Criteria
Finish 10+2 with Physics and Mathematics as required and select either Chemistry, Biology, Biotechnology or Computer Science.

You must get at least 45% in your qualifying examination.

To be eligible for lateral entry into the second year, candidates must own either a 3-year Diploma in engineering or a B.Sc. with Mathematics on their resume.

8. $a_n=\frac{n^2}{2^n}$

Put n=7,

$a_7=\frac{7^2}{2^7}=\frac{49}{128}$

The examples of Adjectives are:

1. Bangalore is a large city.
2. Ram is an honest man.
3. I ate some pudding.
4. You have no time.
5. Have a good day!
6. Most girls like Barbie dolls.
7. Don't be in such a hurry.
8. The CAT is lazy.
9. I don't like that cafe.
10. There are five mangoes in the fridge.

7. a_n = 4_n – 3.

Putting n = 17, we get

a₁₇ = 4 * 17 – 3=68 – 3 = 65.

and putting n = 24 we get,

a₂₄ = 4 * 24 – 3 = 96 – 3 = 93

Raghu Engineering College offers BTech for four-years at the UG level. The course is divided into eight semesters. Candidates after completing Class 12 can apply for any of the below-mentioned BTech specialisations:

• Computer Science
• CSE-Data Science
• CSE-AI & ML
• CSE-Cyber Security
• Electronics & Communication
• Mechanical Engineering etc.

PES University offers UG, PG and Doctoral level courses in full-time mode. The University offers courses such as BSc, BCA, BDes, BTech, BPharma and many more in UG level. Whereas, in PG level, the University offers MTech, MCA, MBA and MPharma. Courses such as BTech, MBA and BSc are the most popular ones among the students. The University offers respective courses in the field of Engineering, Medicine, Architecture, Design, Management and Commerce, Economics and many more.