Question : The sum of 10 terms of the arithmetic series is 390. If the third term of the series is 19, find the first term:
Option 1: 3
Option 2: 5
Option 3: 7
Option 4: 8
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Correct Answer: 3
Solution : Given: The sum of 10 terms of the arithmetic series is 390. So, $n=10$ The third term of the series is 19. Let the first term of the series be $a$. We know, sum of arithmetic progression (A.P.) = $\frac{n}{2}[2a+(n-1)d]$ $n^{th}$ term = $a+(n-1)d$ So, $3^{rd}$ term ⇒ $a+(3-1)d=19$ ⇒ $a+2d=19$ ----------------------------(1) Sum of 10 terms = $\frac{10}{2}[2a+(10-1)d] =390$ ⇒ $2a+9d=78$ ---------(2) Multiplying 9 with equation (1) and 2 with equation (2), we get, ⇒ $9a+18d=171$ ------------------------(3) ⇒ $4a+18d=156$ ------------------------(4) Subtracting (4) from (3), we get, $5a=15$ $\therefore a=3$ Hence, the correct answer is 3.
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Question : What is the sum of the first 9 terms of an arithmetic progression, if the first term is 7 and the last term is 55?
Option 1: 219
Option 2: 137
Option 3: 231
Option 4: 279
Question : The sum of the first 20 term of the series $\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+....$ is:
Option 1: 0.16
Option 2: 1.6
Option 3: 16
Option 4: 0.016
Question : Find the value of the given expression: $10 \div 5 × 1+3 - [8 - \{5 - (7 - 7 - 9)\}]$
Option 1: 11
Option 2: 10
Option 3: 9
Question : The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:
Option 1: 4
Option 3: 14
Option 4: 20
Question : What is the sum of the first 20 terms of the following series? $1 \times 2+2 \times 3+3 \times 4+4 \times 5+\ldots \ldots$
Option 1: 3160
Option 2: 2940
Option 3: 3240
Option 4: 3080
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