# Test: Arithmetic and Geometric Series - Ambitious

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Question 1:   Specify the formula for the arithmetic progression
${a}_{n}={a}_{1}+n$
${a}_{n}={a}_{1}+d×n$
${a}_{n}={a}_{1}+d×\left(n-1\right)$
${a}_{n}=2×{a}_{1}+d×\left(n-1\right)$
Question 2:   Find the twenty-first arithmetic term of the following arithmetic series  $1,1.5,2,...$
$10.5$
$12$
$11$
$10$
Question 3:   Find the common ratio of geometric progression if the first element is  $2$ ,  and the fifth  $1250$ .
$10$
$25$
$2$
$5$
Question 4:   Find the sum of the first hundred members of the arithmetic progression if the first element is  $3$  and the difference is  $5$ .
$25050$
$50100$
$25005$
$25000$
Question 5:   In geometric progression we have:  ${b}_{1}=2$ ,  $q=0.5$ .  Calculate the sum of the first 3 members of the progression.
$3.75$
$2.5$
$4$
$3.5$
Question 6:   Find the fifth term of geometric progression  $2,4,8,...$
$32$
$16$ 
$28$
$64$
Question 7:   In arithmetic progression  ${a}_{7}=10$ ,  ${a}_{11}=16$  calculate the progression difference.
$1.4$
$2$
$3$
$1.5$
Question 8:   In arithmetic progression  ${a}_{10}+{a}_{16}=16$ ,  calculate  ${a}_{13}$ .
$6$
$10$
$4$
$8$
Question 9:   In geometric progression  ${b}_{10}=3$ ,  find  ${b}_{8}×{b}_{12}$
$27$
$6$
$9$
$15$
Question 10:   Calculate the sum of the first twenty natural even numbers.
$422$
$400$
$416$
$420$