Question

If for an A.P S₃₁=2604 find the 16th term.

Answer 1

Step-by-step explanation:

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Answer 2

Given:-

$\sf S_{31}$ = 2604

To find:-

• 16th term.

Formula:-

$\underline{\boxed{\sf S = \dfrac{n}{2} × 2a+(n-1)d}}$

here,

• $\sf S_{31}$ = sum of the terms
• a = 1st term
• n = no. of terms
• d = common difference

Solution:-

$\longrightarrow$ 2604 = $\sf\dfrac{31}{2}$ × 2a+30d

$\longrightarrow$ $\sf\dfrac{2604×2}{31}$ = 2a+30d

$\longrightarrow$ 168 = 2a+30d

$\longrightarrow$ 84 = a+15d

Now,

$\sf a_{16}$ = a+15d

hence, the value of 16th term is 84

Additional information:-

to find the value of a term i.e $\sf a_{n}$, following formula is used:-

$\underline{\boxed{\sf a_{n} = a+(n-1)d}}$

here,

• $\sf a_{n}$ = nth term
• a = 1st term
• n = no. of term
• d = common difference