The second term of a gp is 3 and the fifth term is 818 find...

The second term of a G.P. is 3 and the fifth term is 81/8. Find the eighth term.The first term of a G.P. is 375 and the fourth term is 192. Find the common ratio and the sum of the first four terms.

Transcript

00:01 And this given that second term of a gp is 3 so t2 equal to 3 and the fifth term is at 1 by 8 t5 81 by 8 so find the 18th 8th term the first term okay 8th this is a r raised to the power 1 equals to 3 equal to 81 by 8 okay so let us divide a r raised the power 4 divide by a r equal to 81 by 8 into 3 27 okay this is r q so r will be equal to 3 okay if r is 3 a which is first term we can take we can write plug in anywhere r will be equal to 3 by a and a will be equal to three by r the three by four okay and second question says the okay so i and this is we need to find eighth term a eight or t eight it'll be a r d to the power seven three by four three is to the power seven so three and two four raised to the power okay this is three by four 3x2 x2 x2 the power 7 so this is 3 to the power 8 divide by 4 okay not like this it should be 3 into 3 to the power 7 divide by 4 okay second is the first term of a gp 35 4 term is 192 find the commendation sum of first 4 terms basically it is given that first term a equal to 375 fourth a 4 a 4 equal to 192 a r raised the power 3 equal to 192 r will be equal to 192 by 375 64 by 375 r will be equal to 65 by 375 under root of 375 19 .36 4 by 19 .36 this is the very bar you have to find common ratio and sum this is the common ratio and the sum will be equal to find the common ratio first time already given so sum of first four terms as for will be equal to 1 minus a divide by 1 minus a power n okay so if we plug in 1 minus a is equal to 375 in this case a is 375 1 minus 375 raised to the power 4 divide by 1 minus 375 35 375 minus 1 1 minus r raised the power in by 1 minus r raised to the power n by 1 minus r raised to the power in by r is 64 by 365 4 by 19 .36 raised to the power n divided by 1 minus 4 by 36 okay now if we just use it because this should be r they should be r okay so total sum would be to 19 .36 minus 4 okay like power n means 4 okay another way 19 .36 6 divide by 4 into 1 minus r 19 .36 it is 4 is 4 to part 4 19 .36 minus 4 19 .36 19 .36 9 .3 6 divided minus 4 divided by 19 .36 minus 4 minus 4 minus 3 .206x divided by 19 .3 .3 6 minus 4.

07:41 Divide by 90 .3 step divided by 8.

07:50 0 .0 .2...

Question

The second term of a G.P. is 3 and the fifth term is 81/8. Find the eighth term.The first term of a G.P. is 375 and the fourth term is 192. Find the common ratio and the sum of the first four terms.

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