Question

In an ap given a=7 ,a13= 35 find d and s13

Answer 1

$\rm\green{\underbrace{ Question : }}$

In an ap given a=7 ,a13= 35 find d and s13

$\rm\green{\underbrace{ Solution : }}$

★ Given that,

• a = 7
• a13 = 35 (an)
• n = 13

★ To find,

• Common difference (d)
• Sum of 13 terms.

★ Let,

$\bf\:\implies a_{13} : a + 12d = 35$

$\bf\:\implies 7 + 12d = 35$

$\bf\:\implies 12d = 35 - 7$

$\bf\:\implies 12d = 28$

$\bf\:\implies d = \frac{28}{12}$

$\bf\:\implies d = \frac{7}{3}$

Hence, common difference (d) = 7/3.

★ Now,

$\bf\: Sum \: of \: 13 \: terms :$

By using Sum of nth terms of AP :

$\rm\:\implies S_{n} = \frac{n}{2} [a \: + a_{n} ]$

• Substitute the values.

$\bf\:\implies S_{13} = \frac{13}{2} [ 7 + 35 ]</p><p>$

$\bf\:\implies S_{13} = \frac{13}{2} [ 42 ]$

$\bf\:\implies S_{13} = 13 \times 21</p><p>$

$\bf\:\implies S_{13} = 273$

Hence, it is solved...