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The second and seventh term of a G.P are 18 and 4374 respectively.

Find the common ration
Sum of the 4th and 8th terms
Sum of the first 10th terms

ar = 18

ar^6 = 4374
divide them:
r^5 243 = 3^5
so r = 3

now you can find a, and using your definitions all the other parts asked for

Did you know?

Did you know that in a geometric progression (G.P), the second term is obtained by multiplying the first term by the common ratio? Similarly, the seventh term can be found by multiplying the second term (which is obtained by multiplying the first term by the common ratio) by the common ratio again. In this G.P, the second term is 18 and the seventh term is 4374. By finding the common ratio, we can determine the multiplier used to obtain each term in the progression. Additionally, did you know that the sum of the fourth and eighth terms in a G.P can be calculated by adding the individual terms together? Finally, the sum of the first ten terms in a G.P is the total when all the terms from the first to the tenth term are added together. By understanding these concepts, we can better analyze and solve problems involving geometric progressions.