Question

The first and the last terms of an AP are 10 and 70
, respectively, and the common difference is 5.

(a) Find the number of terms.
(b) Find the sum of the terms.​

Answer 1

Answer:

Total terms are 13 and their sum is 520.

Step-by-step explanation:

First term (a) = 10,

Last term (b) = 70

Common difference (d) = 5.

Now,

nth term of an AP = a + (n - 1)*d

70 = 10 + (n - 1)*5

70 = 10 + 5n - 5

70 = 5 + 5n

70 - 5 = 5n

n = 65/5

n = 13

Therefore,

sum = n*(a+b)/2

= 13 *(10+70)/2

= 13* (80/2)

= 13* (40)

= 520

So, total terms are 13 and their sum is 520.