Explanation:
Prior to attempting the questions below, make sure you notice a somewhat clear pattern.
we can see that the 1st term (5) can yield the second term if we only multiply it by 4.
This kind of series is called a geometric series.
the following formulas are only applicable on a geometric series.
a) Sum formula - Sn = G1 (1 - r^n) / (1 - r)
substitute the number given in subquestion a into n of the formula to find the nth sum.
S10= G1( 1 - r^10) / (1 - r) G1 = 1st term. r = common ratio.
= 5 ( 1 - 4^10) / (1 - 4)
= 349525
b) G8 = eighth term.
G8 = G1(r)^n-1
= 5 × 4^7
= 81,920.
2. Same pattern ...just getting multiplied by 7 again & again.
a) S7 = 1 ( 1 - 7^7) / 1 - 7
= -823542 / -6
= −137257
b) G11 = G1(r)^10
= 1 × 7^10
= 282475249