Use the distributive property:
![a(c+b)=ab+ac](https://tex.z-dn.net/?f=a%28c%2Bb%29%3Dab%2Bac)
And
![a^n\cdot a^m=a^{n+m}\\\\a=a^1](https://tex.z-dn.net/?f=a%5En%5Ccdot%20a%5Em%3Da%5E%7Bn%2Bm%7D%5C%5C%5C%5Ca%3Da%5E1)
Answer:
Common ratio=1/2
Sum of first 6 terms of an A.P=31.5
Step-by-step explanation:
Let a be the first term and d be the common difference of an A.P
a=4
nth term of an A.P
![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
Using the formula
![a_4=a+3d=4+3d](https://tex.z-dn.net/?f=a_4%3Da%2B3d%3D4%2B3d)
![a_{10}=a+9d=4+9d](https://tex.z-dn.net/?f=a_%7B10%7D%3Da%2B9d%3D4%2B9d)
According to question
We know that
For G.P
=Common ratio
![r=\frac{4+3d}{4+9d}=\frac{4}{4+3d}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%2B3d%7D%7B4%2B9d%7D%3D%5Cfrac%7B4%7D%7B4%2B3d%7D)
![\frac{4+3d}{4+9d}=\frac{4}{4+3d}](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B3d%7D%7B4%2B9d%7D%3D%5Cfrac%7B4%7D%7B4%2B3d%7D)
![(4+3d)^2=\frac{4}{4+3d}](https://tex.z-dn.net/?f=%284%2B3d%29%5E2%3D%5Cfrac%7B4%7D%7B4%2B3d%7D)
![16+9d^2+24d=16+36d](https://tex.z-dn.net/?f=16%2B9d%5E2%2B24d%3D16%2B36d)
![9d^2+24d-36d-16+16=0](https://tex.z-dn.net/?f=9d%5E2%2B24d-36d-16%2B16%3D0)
![9d^2-12d=0](https://tex.z-dn.net/?f=9d%5E2-12d%3D0)
![3d(3d-4)=0](https://tex.z-dn.net/?f=3d%283d-4%29%3D0)
![d=0, d=4/3](https://tex.z-dn.net/?f=d%3D0%2C%20d%3D4%2F3)
Substitute the value of d
When d=0
![r=\frac{4}{4+3d}=\frac{4}{4+0}=1](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B4%2B3d%7D%3D%5Cfrac%7B4%7D%7B4%2B0%7D%3D1)
When d=4/3
![r=\frac{4}{4+3\times \frac{4}{3}}=\frac{1}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%7D%7B4%2B3%5Ctimes%20%5Cfrac%7B4%7D%7B3%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D)
But we reject d=0 because if we take d=0 then the terms are not consecutive terms of G.P
Sum of n terms of an A.P
![S_n=\frac{n}{2}(2a+(n-1)d)](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%282a%2B%28n-1%29d%29)
Using the formula
Substitute n=6 and d=1/2
![S_6=\frac{6}{2}(2(4)+5\times \frac{1}{2})](https://tex.z-dn.net/?f=S_6%3D%5Cfrac%7B6%7D%7B2%7D%282%284%29%2B5%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%29)
![S_6=31.5](https://tex.z-dn.net/?f=S_6%3D31.5)
Answer:
So,
![g(x) = 3x - 1](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%20-%201)
And,
![g(a) = 3a - 1](https://tex.z-dn.net/?f=g%28a%29%20%3D%203a%20-%201)
But, given g(a) = 7
So, from 2nd and 3rd step,
3a-1=7
3a=6
Therefore, a = 2
Answer:
sgsgzhzhdhenovavjejvoogjqou2jgjqhj
Step-by-step explanation:
123344
The answer is C hope it helps have a wonderful day/night'