In an AP if the sum of 4th and 8th terms is 70 and its 15th term is 80 then find the sum of its first 25 terms some one

answer fast plzzzzzz its urgent

Question

In an AP if the sum of 4th and 8th terms is 70 and its 15th term
is 80 then find the sum of its first 25 terms some one
answer fast plzzzzzz its urgent

Ajanta Trivedi · Accepted Answer

let the first term and the common difference of AP be a and d respectively.

4th term of the AP = a+(4-1)d=a+3d

8th term of AP = a+(8-1)d=a+7d

therefore

$a + 3 d + a + 7 d = 70 2 a + 10 d = 70 a + 5 d = 35............ (1)$

15th term = 80

therefore

a+(15-1)d=80

a+14d=80.......(2)

solving (1) and (2):

-9d=-45

d=45/9=5

a+5*5=35

a+25=35

a=35-25=10

thus the first term is 10 and the common difference is 5.

sum of n terms = $\frac{n}{2} [2 a + (n - 1) d]$

sum of 25 terms = $\frac{25}{2} [2 * 10 + (25 - 1) * 5] = \frac{25}{2} [20 + 120] = \frac{25}{2} * 140 = 1750$

hope this helps you.

In an AP if the sum of 4th and 8th terms is 70 and its 15th term is 80 then find the sum of its first 25 terms some one answer fast plzzzzzz its urgent

In an AP if the sum of 4th and 8th terms is 70 and its 15th term is 80 then find the sum of its first 25 terms some one

answer fast plzzzzzz its urgent