UrbanPro
true

Take Class 10 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Arithmetic Progression Examples

Ashish K Sharma
23/02/2023 0 0

                                             Arithmetic Progression Examples.

Q: A man starts repaying a loan, with Rs 100 being its first instalment. If he increases the instalment by Rs 5/- every month, what amount he will pay in the 30th instalment?

 

                                                                  Solution:

 

We know that the last  term of an AP is given by:

                                   l = (a+ (n-1) * d).      ….. (1)

 

Now, as per the question,

                                          a = 100,d = 5 and n = 30.

  • l = (100 + (30-1) * 5) substituting the values in expression (1)
  • l = 245

 

Thus, the amount to be paid in the 30th instalment will be Rs 245/-

***************************************************************

 

Q2. The Sum of the first four terms of an AP is 56, and, the sum of the last 4   

       terms is 112. If its first term is 11 then find out the number of terms of the

       series.

 

 

                                                    SOLUTION.

 

We know that the Sum of the first n terms of an AP is given by:

                                   Sn = (n / 2) * ((2 * a + (n-1) * d)). ……. (1)

 

Now, as per the question, substituting the relevant values in (1), we have,

  • = (4 / 2) * ((2 * 11 + (4-1) * d)).
  • 56 = 44 + 6d
  • d = 2

Thus, now we have the first term as 11 and the common difference as 2.

Now, the last 4 terms of a AP is:  a + (n-1) * d, a + (n-2) * d , a + (n-3) * d and a + (n-4) * d.

Now, as per the question,

a + (n-1) * d + a + (n-2) * d + a + (n-3) * d + a + (n-4) * d = 112

  • 4a+4nd – 10d = 112
  • 2d(2n – 5) + 4 * 11 = 112 (substituting d = 2,a = 11)
  • 4(2n-5) + 4 * 11 = 112
  • 8n-20+44 = 112
  • 8n = 112 – 24 = 88
  • n = 11

Thus, the number of the terms of the series is 11.

0 Dislike
Follow 1

Please Enter a comment

Submit

Other Lessons for You

Game Theory
Trees, frames and gamesOften interactions are not simultaneous but sequential. For example, in Chess's game, the two players, White and Black, take turns moving pieces on the board, having full knowledge...

Ohm's law and its calculations
Ohm's Law states that voltage is directly proportional to current and resistance V=IR Here, V is Voltage I is Current R is Resistance Using the the mnemonics you can easily know by " Very Interesting...

verb formations
लट् लकार (वर्तमान काल, Present Tense) पुरुष एकवचन द्विवचन वहुवचन प्रथम पुरुष ति तस् (तः) अन्ति मध्यम...

Dhaturoop with meaning
विधिलिड्. लकार: (possibility and prayer ) पुरुष: एकवचनम् अर्थ द्विवचनम् अर्थ बहुवचनम् अर्थ प्रथमपुरुष: पठेत् पढ़ना चाहिए पठेताम् (दो को )...

Area of the Triangle Using Base & Height
HOW TO FIND THE AREA OF THE TRIANGLE WHEN BASE & HEIGHT ARE GIVEN if the base of the triangle = b and height of the triangle = h then, area of the triangle = (1/2) x b xh square units Ex:- if...
X

Looking for Class 10 Tuition Classes?

The best tutors for Class 10 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 10 Tuition with the Best Tutors

The best Tutors for Class 10 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more