Question

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

Answer 1

Step-by-step explanation:

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Answer 2

Number of terms ,n=5

Step-by-step explanation:

Let first three terms

a,a+d and a+2d

Sum of first three term=30

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

$3a+3d=30$

$3(a+d)=30$

$a+d=\frac{30}{3}=10$

First term,a=9

Substitute the value of a

$9+d=10$

$d=10-9=1$

Sum of last three terms=36

nth term of A.P

$a_n=a+(n-1)d$

Using the formula

$a_n=9+(n-1)(1)$

$a_n=9+n-1=8+n$

Last second term=n+8-1=n+7

Last third term=n+7-1=n+6

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

$3n+21=36$

$3n=36-21=15$

$n=\frac{15}{3}=5$

Therefore, number of terms ,n=5

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