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Question

Q1. What is the sum of the ﬁrst 7 terms of the series 1/3, 1/2, 3/4, …?

1. 2059/164
2. 2050/192
3. 2059/164
4.  None of these

Q2. The sum of 15 terms of an AP is 600, and the common difference is 5. Find the ﬁrst term

1. 4
2. 5
3. 3
4. None of these

Sum of an AP $= \frac{n}{2}\left ( 2a+\left( n-1 \right )d \right )$

= 600= 15/2 (2a+ 14*5)

= By solving, we get a=5.

Q3. A man arranges to pay off a debt of `3600 by 40 annual installments which form an AP. When 30 of the installments were repaid, he died leaving a third of the debt unpaid. What is the value of the first installment

1. 50
2. 51
3. 52
4. 53

let,

First Installment = a,  and common difference = d

= 3600=40/2 (2a+39d)

2a+39d= 180…..I

And,

30 installments were repaid, he died after living third debt unpaid,

= 3600/3 = 10/2 (2(a+30d)+9d)

= 1200 = 5 (2a+69d)

= 2a+69d = 240…..II

From Eq. I and II

a = 51, and d = 2

Q4. The first term in a sequence of integers is 2 and the second term is 10. All subsequent terms are the arithmetic mean of all of the preceding terms. What is the 39th term?

1. 5
2. 6
3. 600
4. 300

The first term and second term average out to 6. So the third term is 6. Now add 6 to the preceding two terms and divide by 3 to get the average of the first three terms, which is the value of the 4th term. This, too, is 6 (18/3)—all terms after the 2nd are 6, including the 39th. Thus, the answer is 6.

Q5. The sequence a1+a2+...+an begins with the numbers 3,11,18,... and has the nth term defined as a1+2n+n2, for n2.

What is the value of the 20th term of the sequence?

1. 155
2. 460
3. 220
4. 443

The first term of the sequence is a1, so here a1=3, and we’re interested in finding the 20th term, so we’ll use n = 20.

Plugging these values into the given expression for the nth term gives us our answer

a1 + 2n2+n2

a1=3 and n=20

3 + 2(20) + 202=443

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