Question

The 4th term of an ap is 18 and the common difference is -5. find the (i) first term and (ii) the sum of the first sixteen terms​

Answer 1

Explanation:

(i) The formula for arithmetic progressions is = a+(n-1)d.

This formula can be used to find out the value of any term in the progression by changing the value of n. Here, n is the term we need to find out, d is the common difference and a is the first term.

To find out the first term, using this formula and the value of the fourth term: a=?; d=-5; n= 4.

So, it becomes => a+(4-1)(-5)=18

=> a + 3(-5) = 18

=> a+(-15) = 18

=> a= 18+15

=> a= 33

So, the first term in this A.P. is 33.

(ii) The formula for the sum of an A.P. is = n/2 {2a+(n-1)d}.

All the terms are the same as the first formula here.

So, a=33 ; n= 16 ; d=-5.

So, it becomes => 16/2 {2(33) + (16-1)(-5)}

=> 8 {66 +(-75)}

=> 8 (-9)

=> -72

So, the sum of the first sixteen terms is -72.