Find the sum of the first 7 terms of the series. 6-12+24-48+

258

Step-by-step explanation:

Since, the sum of GP is,

where r is the common ratio,

a is the first term,

n is the number of term,

Here, series is, 6, -12, 24, -48, _ _ _ _

Which is a GP ( Because there is common ratio in the given consecutive terms )

So, for the above series,  a = 6, r =  and  n = 7,

⇒

⇒

⇒

⇒

Thus, the sum of the 7 terms of the given series is 258.

d

step-by-step explanation:

d

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°