Question

Find the value of n if 102 +97 +92 +
to n terms = 1090. Also find tn.​

Answer 1

Answer:

999

Step-by-step explanation:

102,97,92,... up to 27 terms.

a = 102

d = a² - a¹

d = 97 - 102

d = - 5

We know That,

sn = n/2 {2a + (n-1)d}

Now, according to given information

sn = 27/2 {2 × 102 + (27-1)-5}

sn = 27/2 (204 + 26 × -5)

sn = 27/2 (204 - 130)

sn = 27/2 × 74

sn = 27 × 37

sn = 999

Hence,

sum of the following terms is -

sn = 999

I hope you will find this helpful dear

Good Luck :)

Answer 2

Here a = 102, d = -5

Sn = (n/2) × [2a + (n-1)d]

= (n/2) × [204 - (n-1)5]

= (209n - 5n²)/2

209n - 5n² = 1090 × 2

5n² - 209n + 2180 = 0

After solving the quadratic equation , we get the value of n = 20.

T20 = 102 + (20-1)(-5) = 102 - 95 = 7