 a4 is equal to 10, 7 is equal to 80, and an is equal to 2560, okay. Find a1, a4 is 10, this is for a GP, not for an AP, this is for a, fourth term is 10, seventh term is 80, second term is 2560, a4, these are all, only one formula, what is this an is equal to a1 or ar to the power n minus 1, so a4 is 10, so a4 is ar cube, a7 is ar6, now 10 is equal to ar cube, 80 is equal to ar6 or 6 divided, 1 upon 8 is equal to 1 upon ar cube, right, so ar is clearly 2, ar is 2, so when ar is 2 you can find out a, what is a, take any equation let's say this one, so a4 is 10 is equal to a2 to the power of 3, so a is 10 upon 8, it is 1.25, what are you going to leave it like that 5 by 4, correct, then you have to find out an is equal to ar n minus 1 and this is 2560, correct, so 2r n minus 1 is equal to and ar is what 2, so you can write 2 here directly, so 2 to the power n minus 1, a was how much, 5 by 4 is equal to 2560, you have to find out n, so this 5 by 4 goes becomes 4 by 5 here, right, so and I will multiply this by 2, by 2, so this becomes 10 and this 0 goes, okay, so hence it is 2 to the power n minus 1 is equal to 2 to the power 8, it is into 2 to the power 3, 4 into 2, yeah, so 8, so n minus 1 is nothing but 8 plus 3, so n is 12, a is equal to 1 given first term, okay, and a3 plus a5, third term and fifth term sum is 90, find r, find r, so first term is given as 1, third term plus fifth term sum is 90, find r, very easy, what was a3, a3 is ar square plus a5 is ar4, right, a3 plus a5 and this is 90, so basically a was 1, so r square plus r to the power 4 is 90, this equation you have to solve and it is simply r4 plus r square minus 90, so split the middle term you will get r4 plus 10 r square minus 9 r square minus 90 is 0, yes, so r square common r square plus 10 minus 9 r square plus 10 is 0, okay, so hence r square plus 10 is into r square minus 9 is 0, okay, in our series, in sequences we are only dealing with real numbers, no complex numbers, okay, so r square plus 10 cannot be real, cannot be 0, sorry, it can be real but not equal to 0, because r square is positive and 10 added to a positive number will never be 0, so this is 0, so then that means r is plus minus 3, right, in the same question they are asking you both concepts of GP as well as quadratic, these are the nature of questions which you will see, okay.