alleryThe 6th term is 23 and the common difference is 4. What is the first term?
- −1
- 3
- 7
- 11
Show answer and solution
Correct answer: B. 3
The first term is 23−5×4=3.
ICSE Class 10 Arithmetic & Geometric Progressions — practice questions — page 2
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.
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Showing questions 31–60 of 81.
The 6th term is 23 and the common difference is 4. What is the first term?Read the answer and worked solution →Calculate the sum of the first 20 terms of 3, 7, 11, … .Read the answer and worked solution →How many terms of 2, 5, 8, … have a total of 345?Read the answer and worked solution →An AP has 13 terms, from 7 to 55. What is their sum?Read the answer and worked solution →Which term of the AP 2, 5, 8, … is 38?Read the answer and worked solution →Insert the arithmetic mean between 8 and 20.Read the answer and worked solution →An AP has S10=245 and common difference 3. Find its first term.Read the answer and worked solution →The GP 3, 6, 12, … continues. What is its 6th term?Read the answer and worked solution →Starting with 2 and multiplying by 3 each time, what is the 7th term?Read the answer and worked solution →A GP has first term 5 and common ratio 2. Find its 6th term.Read the answer and worked solution →Write out 3 + 6 + 12 + 24 + 48 as one total.Read the answer and worked solution →A GP starts 3, −6, 12, −24. Find the sum of these four terms.Read the answer and worked solution →For positive x, if 4:x = x:36, what is x?Read the answer and worked solution →A positive-ratio GP starts at 4 and its 5th term is 324. Find the ratio.Read the answer and worked solution →Starting at 81 and dividing each term by 3, what is in position 5?Read the answer and worked solution →In the GP 5, 10, 20, …, which term is 640?Read the answer and worked solution →Evaluate the finite series 1 + 3 + 9 + 27.Read the answer and worked solution →A nonzero constant sequence 7,7,7,… is an AP with common differenceRead the answer and worked solution →Which formula defines an AP for positive integers n?Read the answer and worked solution →An AP has difference 4. The subsequence a₁,a₄,a₇,… has differenceRead the answer and worked solution →A finite AP has common difference −3. Reversing its order gives differenceRead the answer and worked solution →For an AP, first-five sum S₅=60 and first-four sum S₄=44. Fifth term?Read the answer and worked solution →An AP has S₁₂=180 and S₄=28. Sum of terms fifth through twelfth?Read the answer and worked solution →A 12-term AP begins with 3 and ends with 47. What is a₄+a₉?Read the answer and worked solution →x−2,2x+1,5x−4 are consecutive terms of an AP. Find x.Read the answer and worked solution →An AP has a>0,d>0 and a₃:a₇=2:5. Find a:d.Read the answer and worked solution →For an AP with a,d>0, S₁₀=3S₅. What is a:d?Read the answer and worked solution →An AP has 2n terms, first a and last l, n a positive integer. Its mean isRead the answer and worked solution →Which sequence is geometric?Read the answer and worked solution →Sum n terms of the constant GP a,a,a,…, where a≠0,n≥1.Read the answer and worked solution →
Worked practice questions
Calculate the sum of the first 20 terms of 3, 7, 11, … .
- 780
- 800
- 820
- 840
Show answer and solution
Correct answer: C. 820
The twentieth term is 79, so the sum is 20(3+79)/2=820.
How many terms of 2, 5, 8, … have a total of 345?
- 12
- 14
- 15
- 16
Show answer and solution
Correct answer: C. 15
The sum formula gives n(3n+1)=690, whose positive integer solution is n=15.
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