Question

the 13th term of an arithemetic progression is 3 and sum of the first 13th term is 234 find first term​

Answer 1

Answer:

Sn = n/2(tn+a)

234=13/2(3+a)

468=13(3+a)

468/13=3+a

36=3+a

a=33

Answer 2

Answer:

The first term of A.P. = 33

Step-by-step explanation:

Given that -

The 13th term of arithmetic progression (A.P.) = 3

Sum of first 13th term = 234

We know that -

The sum of n term $S_{n}$ = $\dfrac{n}{2}[a+l]$

Where a = first term of A.P.

l = last term of A.P.

n = total terms of A.P.

We have l = 3 and n = 13

234 = $\dfrac{13}{2} [ a + 3]$

234 × 2 = 13 [ a + 3 ]

$\dfrac{234 \times 2}{13}$ = a + 3

18 × 2 = a + 3

a + 3 = 36

a = 36 - 3

a = 33

Hence the first term of A.P. is 33