Question

The first and the last term of an A.P are -4 and 146 and the sum of A.P is 7171. Find the number of
terms in the A.P and common difference.

Answer 1

a1=-4
an=146
Sn=7171

an=a+(n-1)d
150=(n-1)d

7171=n/2(2a+(n-1)d)
101=n


no. of terms are 101

d

150=(n-1)d
put value of n
d=3/2...


hope it will help...

Answer 2

Answer:

$\huge{\boxed{\boxed{\sf{n=101\:and\:d=1.5}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

□a=-4

□l=146

□Sn=7171

To find:

○n=?

○Common difference=?

$sn = \frac{n}{2} (a + l) \\ = ) 7171 = \frac{n}{2} ( - 4 + 146) \\ = )2(7171) = n(142) \\ = )n = \frac{2(7171)}{142} \\ = )n = \frac{7171}{71} \\ = )n = 101 \\ \\ again \\ l = a + (n - 1) \times d \\ = ) 146 = - 4 + (101 - 1) \times d \\ = )146 + 4 = 100 \times d \\ = )150 = 100d \\ = )d = \frac{150}{100} \\ = )d = 1.5$

$\huge{\boxed{\boxed{\sf{n=101\:and\:d=1.5}}}}$