Question

35. Form an Arithmetic progression consists of 'n' terms, the sum of first three terms of
Apis 30 and the sum of last three terms is 36. If the first term is 9 then find number of terms ​

Answer 1

Given,

first term(a) = 9

n = no. of terms

d = common difference

an = nth term (last term)

Sum of first 3 terms= 30

Objective: to form an ap.

Let the first three terms=

a, a+d, a+2d.

thus,

sum of first 3 terms=

a+a+d+a+2d= 30

3a+ 3d= 30

a+d= 10

d= 10-a = 1

thus,

common difference= 1

thus,

nth term= a +(n-1)d

=> 9 + n-1 = n+8

thus,

last term= n+8

second last term = n+7

third last term = n+6

thus,

n+8+n+7+n+6=36

3n+ 21=36

n= 15/3 = 5 terms.

ap:

a = 9

a+d =10

a+2d =11

a+3d =12

a+4d =13

Answer 2

hope it is helpful for you !!!!!!!!