The 1st term of geometric sequence is 4. What is the total sum of the 1st 6 term of the series? 'A' H Common…

Question

The 1st term of geometric sequence is 4. What is the total sum of the 1st 6 term of the series? 'A' H Common ratio 3

ScanSolve AI Tutor · Accepted Answer

Hili ni swali kuhusu mfululizo wa kijiometri (geometric sequence). Tutatumia formula ya jumla ya vigezo vya mfululizo wa kijiometri.

Formula ya jumla ya $n$ vigezo vya kwanza vya mfululizo wa kijiometri ni:

S_n = \frac{a(r^n - 1)}{r - 1}

ambapo $a$ ni kigezo cha kwanza, $r$ ni uwiano wa kawaida (common ratio), na $n$ ni idadi ya vigezo.

Tambua vigezo vilivyotolewa.
Kigezo cha kwanza ( $a$ ) = 4
Idadi ya vigezo ( $n$ ) = 6
Uwiano wa kawaida ( $r$ ) = 3
Badilisha vigezo hivi kwenye formula ya jumla ya vigezo vya mfululizo wa kijiometri.
$S_6 = \frac{4(3^6 - 1)}{3 - 1}$
Fanya hesabu ya $3^6$ .
$3^6 = 729$
Badilisha thamani ya $3^6$ kwenye formula na urahisishe.
$S_6 = \frac{4(729 - 1)}{2}$ $S_6 = \frac{4(728)}{2}$ $S_6 = 2(728)$ $S_6 = 1456$
Jumla ya vigezo 6 vya kwanza ni:
$1456$

The 1st term of geometric sequence is 4. What is the total sum of the 1st 6 term of the series? 'A' H Common ratio 3