Question

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24. The first term of an A.P. is 20 and the sum
of its first seven terms is 2100; find the 31s
term of this A.P.
10 and​

Answer 1

$\green{\underline\textbf{Given...}}$

a1 = 20

S7 = 2100

$\green{\underline\textbf{To find...}}$

The value of 31st term of the Ap...

$\green{\underline\textbf{SoLution...}}$

Sn = n/2 ( 2a + ( n - 1 ) × d )

2100 = 7/2 ( 2(20) + ( 7 - 1 ) × d )

300 = 1/2 ( 40 + 6 × d )

300 × 1/2 ( 40 + 6 × d )

600 = 40 + 6d

300 = 20 + 6d

15 = 6d

15 / 6 = d

Since, we have the value of a and d both...So, we can find the value of 31st term of an Ap...

a + 30d

20 + 30 ( 15/6)

= 95

Therefore, 31st term of an Ap will be 95...