Question

there are 60 terms in a finite A. P. Its first term is 7 and the last term is 125.Find its 32nd term

Answer 1

Given that the AP which is given in the question is a finite AP and its first term is 7 and last term is 125.



First term = a = 7

last term = $a_{l}$=125

Number of terms = l = 60

common difference = d = not given




We know, $a_{n}=a+(n-1)d$



Applying this formula and assuming last term of the given AP as nth term of the AP.

$a_{l}= a+(l-1)d$

$125=7+(60-1)d$

$125-7=59d$

$118=59d$

$\dfrac{118}{59}=d$


$2 = d$




Therefore, common difference between the given APs is 2



$\: \: \underline{applying \: the \: same \: formula \: again}$


32nd term = 7 + ( 32 - 1 )( 2 )

32nd term = 7 + 31( 2 )

32nd term = 7 + 62

32nd term = 69

Answer 2

The 32nd term of AP is 69