Question

the sum of first n terms of an AP is 3n^2+5n. find which Term of AP is 152 and find the sum of first 20 terms​

Answer 1

Answer:

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Answer 2

The sum of first 20 terms​ = 1300 and $25^t^h$ term is 152.

Given:

The sum of first n terms of an AP is $3n^2$+5n.

To find:

Which Term of AP is 152.

The sum of first 20 terms​.

Explanation:

The sum of first 20 terms​.=  $3n^2$+5n.

                                           =  $3\times 20^2$+5×20

                                           = 3 × 400 + 100

                                           = 1300

Which Term of AP is 152.

$S_1$ = $3n^2$+5n. = 3×1+5×1 = 8

That is first number = 8

$S_2$ = $3n^2$+5n. = 3 × 2² +5×2 = 12+10 =22

$S_2$ = $a_1$ + $a_2$

22 = 8+$a_2$

$a_2$  = 22-8 = 14

Common difference = $a_2$ - $a_1$  = 14-8 = 6

$n^t^h$ term = a+(n-1)d

   152 = 8 + (n-1)6

   152-8 = 6n -6

   144 +6 =6n

      150 = 6n

        n = $\frac{150}{6}$ =25

The sum of first 20 terms​ = 1300 and $25^t^h$ term is 152.

To learn more....

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2)If a b c are in ap then prove that 2a+3, 2b+3, 2c+3 are also in AP

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