Question

The sum of 10th and 11th term of an arithmetic sequence is 65.what is the sum of its first and 20th term?

Answer 1

650

Step-by-step explanation:

t10 + t11 = 65........(i)

S20 = ?

:- tn = a+(n-1)d

t10 = a+(10-1)d

t10 = a+9d..........(1)

now,

t11 = a+(11-1)d

t11 = a+10d.........(2)

Put value of (1) and (2) in (i)

(a+9d) + (a+10d) = 65

2a + 19d = 65........(3)

Sn = n/2[2a+(n-1)d]

S20 = 20/2 [2a + (20-1) d ]

S20 = 10[2a+19d]

S20 = 10(65)........

form (3)

S20 = 650

Therfore, Sum of first 20 terms is 650.

Hope it helps you.