Question

AP is 17 , 21, 25........ find the sum of 130 terms

Answer 1

Answer:

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Answer 2

ANSWER :–

$\\ \: \longrightarrow \: \large { \red{ \boxed{ \bold{ Sum \: \: of \: \: 130 \: \: terms =35,750}}}}$

EXPLANATION :–

GIVEN :–

• An A.P. is 17 , 21 , 25 ..........

TO FIND :–

• Sum of 130 terms of A.P.

SOLUTION :–

• We know that sum of n - terms is –

$\\ \: \implies \large { \pink{ \boxed{ \bold{ S_{n} = \frac{n}{2} [2a + (n - 1)d]}}}}$

• Here –

$\\ \: \large { \blue{ \bold{ \: \: \: . \: \: a \: = \: first \: \: term = 17}}}$

$\\ \: \large { \blue{ \bold{ \: \: \: . \: \: d\: = \: common \: \: difference = 4}}}$

$\\ \: \: { \blue{ \bold{ \: \: \: . \: \: n\: = \: \: number \: \: of \: \: terms = 130}}}$

• Now put the values –

$\\ \: \implies { \bold{ S_{130} = \frac{130}{2} [2(17) + (130 - 1)4]}}$

$\\ \: \implies { \bold{ S_{130} = \frac{130}{2} [34 + 129 \times 4]}}$

$\\ \: \implies { \bold{ S_{130} = \frac{130}{2} [34 + 516]}}$

$\\ \: \implies { \bold{ S_{130} = \frac{130}{2} [550]}}$

$\\ \: \implies { \bold{ S_{130} = 65 (550)}}$

$\\ \: \implies \large { \red{ \boxed{ \bold{ S_{130} =35,750}}}}$