# Test: Arithmetic and Geometric Series - Ambitious

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Question 1:   Specify the formula for the arithmetic progression
${a}_{n}={a}_{1}+d×n$
${a}_{n}={a}_{1}+n$
${a}_{n}={a}_{1}+d×\left(n-1\right)$
${a}_{n}=2×{a}_{1}+d×\left(n-1\right)$
Question 2:   Find the twenty-first arithmetic term of the following arithmetic series  $1,1.5,2,...$
$10$
$11$
$12$
$10.5$
Question 3:   Find the common ratio of geometric progression if the first element is  $2$ ,  and the fifth  $1250$ .
$2$
$10$
$5$
$25$
Question 4:   Find the sum of the first hundred members of the arithmetic progression if the first element is  $3$  and the difference is  $5$ .
$25050$
$25005$
$50100$
$25000$
Question 5:   In geometric progression we have:  ${b}_{1}=2$ ,  $q=0.5$ .  Calculate the sum of the first 3 members of the progression.
$2.5$
$3.75$
$3.5$
$4$
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