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Wittaler [7]
2 years ago
14

The fourth term of an exponential sequence is 108 and the ratio is 3 . Calculate the value of the eighth term of the sequence, c

alculate the sum of the first five terms of the sequence.
Mathematics
1 answer:
Over [174]2 years ago
8 0

Answer:

8th term = 8748 , Sum of 5 terms = 484

Step-by-step explanation:

Formula for nth term in an exponential sequence = a r^ (n-1)

Here : n = 4 , ratio r = 3 ; And nth ie 4th number = 108

So,  a r^ (n-1) = nth item implies that → a 3 ^ (4-1) = 108

a 3^3 = 108 →  27 a = 108 → a = 108 / 27 → a = 4

<u>8th</u><u> term </u>= a r^ (n-1) , at  n = 8.  So, = 4 3^(8-1) = 4 3^7 = 4 x 2187 = 8748

Sum of n terms = a [(r^n) -1 ] / [r - 1] → <u>Sum </u><u>5</u><u> </u>terms = 4 [ (3^5)- 1] / [3 - 1]

= 4 [ (243) - 1] / 2 ] = 2 x 242 = 484

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