Correct Answer
✅ Option b — 1705
All Options:
- A1605
- B1705
- C1805
- DNone of these
Detailed Solution & Explanation
We are given:
Let us find which terms are positive:
So the first positive term is the $10^{}t_{10}\displaystyle ):<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>t</mi><mn>10</mn></msub><mo>=</mo><mo>−</mo><mn>29</mn><mo>+</mo><mn>9</mn><mo stretchy="false">(</mo><mn>3.5</mn><mo stretchy="false">)</mo><mo>=</mo><mn>2.5</mn></mrow><annotation encoding="application/x-tex">t_{10} = -29 + 9(3.5) = 2.5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord">29</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">9</span><span class="mopen">(</span><span class="mord">3.5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.5</span></span></span></span></span><br><br>The number of positive terms is $40 - 9 = 31 terms.
The last term is :
Sum of these $31$ positive terms is:
Hence, **Option B** is the correct answer.
About This Chapter: Sequence and Series
Paper
Paper 3: Quantitative Aptitude
Weightage
4-6 Marks
Key Topics
Arithmetic & Geometric Progressions
This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.
View Official ICAI SyllabusExam Strategy Tip
For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.
Related Comparison Tables
More Questions from Sequence and Series
Sum of progression
Find the sum of first twenty-five terms of A.P. series whose
If the common difference of an AP equals to the first term, then the ratio of its
Find the value of
The first and last terms of an arithmetic progression are
If the sum of
Ready to Master Sequence and Series?
Practice all 213 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.
Start Practicing — It's Free