Question

find the sum of the sequence 72,70,68.....100 terms​

Answer 1

Answer:

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Answer 2

Answer:

Sum of 1st 100 terms of the sequence 72, 70, 68,...... is -2700

Step-by-step explanation:

We are given a Progression,

Now, to find what kind of Progression this is, let's start by finding their common differences,

a2 - a1 = 70 - 72

= -2

a3 - a2 = 68 - 70

= -2

So, when a progression have the same common difference between its successive terms, then it is an Arithmetic Progression. (A.P)

Thus,

AP = 72, 70, 68,.......

Now,

We can find the 100th term using the formula,

a(nth) = a + (n - 1)d

Here,

a(1st term) = 72

d = (-2)

n = 100

a(100th) = 72 + (100 - 1)(-2)

a(100th) = 72 + 99(-2)

a(100th) = 72 - 198

a(100th) = -126

Thus,

AP = 72, 70, 68,........, -126

We can find the sum using the formula,

Sn = (n/2)[a + l]

Here,

a = 72

l (last term) = -126

n = 100

So,

S(100) = (100/2)[72 + (-126)]

S(100) = 50[72 - 126]

S(100) = 50 × (-54)

S(100) = -2700

Thus,

Sum of 1st 100 terms of the sequence 72, 70, 68,...... is -2700.

Hope it helped and believing you understood it........All the best.