alleryA GP starts with a≠0 and has ratio −1. Sum of its first 8 terms?
- −8a
- a
- 0
- 8a
Show answer and solution
Correct answer: C. 0
The four pairs a+(−a) each cancel, giving zero.
ICSE Class 10 Arithmetic & Geometric Progressions — practice questions — page 3
Explore 81 free Arithmetic & Geometric Progressions questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Arithmetic & Geometric Progressions with Quill →Arithmetic & Geometric Progressions questions and exercises with answers
Showing questions 61–81 of 81.
A GP starts with a≠0 and has ratio −1. Sum of its first 8 terms?Read the answer and worked solution →A GP has a>0,r<0. Which term positions have positive values?Read the answer and worked solution →For a>0 and 0<r<1 in a GP, each next term isRead the answer and worked solution →A nonzero GP has ratio 3. Its subsequence a₁,a₃,a₅,… has ratioRead the answer and worked solution →A finite nonzero GP of at least 2 terms has ratio 4. Its reverse has ratioRead the answer and worked solution →In a positive GP, a₃=12 and a₆=96. Find the first term.Read the answer and worked solution →A nonzero real GP has a₂=6,a₄=24. Which common ratios are possible?Read the answer and worked solution →x−1,x+1,x+5 are positive consecutive GP terms. What is x?Read the answer and worked solution →For a GP with first a, ratio r≠1 and positive integer n, Sₙ equalsRead the answer and worked solution →Sₙ=3+6+12+…+3·2ⁿ⁻¹=189. Find the positive integer n.Read the answer and worked solution →A finite GP has first term 5, ratio 3 and sum 200. Its last term?Read the answer and worked solution →In the GP with a=2,r=3, sum the third through sixth terms inclusive.Read the answer and worked solution →A ball drops 8 m; each bounce rises half its last fall. Travel through 3 ground hits?Read the answer and worked solution →An asset keeps 80% of its value each year. Initially ₹500, its value after 3 years?Read the answer and worked solution →Three positive numbers are consecutive terms of both an AP and a GP. They must beRead the answer and worked solution →A GP starts a,ar,ar² with a,r>0. If a+ar=6 and ar+ar²=18, r equalsRead the answer and worked solution →Insert two positive geometric means between 2 and 54. What is the first inserted?Read the answer and worked solution →Match each AP sequence with its common difference d:Read the answer and worked solution →Match each sequence computation with its evaluated answer:Read the answer and worked solution →Match each AP selection strategy with the chosen symmetric variables:Read the answer and worked solution →Match each Arithmetic Progression (AP) formula with its quantity:Read the answer and worked solution →
Worked practice questions
A GP has a>0,r<0. Which term positions have positive values?
- Odd positions only
- Multiples of three
- All term positions
- Even positions only
Show answer and solution
Correct answer: A. Odd positions only
An even exponent n−1 makes arⁿ⁻¹ positive exactly at odd positions.
For a>0 and 0<r<1 in a GP, each next term is
- Positive and larger
- Alternating in sign
- Negative and smaller
- Positive and smaller
Show answer and solution
Correct answer: D. Positive and smaller
Multiplication by a positive fraction preserves positivity while reducing each value.
How to practise
- Choose a Arithmetic & Geometric Progressions question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.
Put it into practice
Continue with Arithmetic & Geometric Progressions practice for ICSE Class 10. Read explanations as you go. No signup form needed to start.
Practise Arithmetic & Geometric Progressions →