Question

12. The sum of the first term and the fifth term
ascending AP is 28 and the product of the se
term and the fourth term is 180. Find the suo.
the first seven terms of this AP.
(1) 133 (2) 115 (3) 140
(4) 12
2.2 on the rati​

Answer 1

ANSWER

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ANSWer

Answer 2

Answer:

Sum of 7 terms = 126

Step-by-step explanation:

Given data

sum of the first term and fifth term in AP = 28

product of the second term and four term = 180

here we need to first 7 terms in given AP

Let  a-2d, a-d, a, a+d, a+2d, a+3d, a+4d are be the first 7 terms of the AP

From given data  1st term + 5th term = 28

                            a-2d +  a+2d = 28

                                          2a = 28

                                           a = 14  

product of 2nd term and 4th term = 180

                           (a-d)(a+d) = 180

                             a² - d² = 180      

                            14² - d² = 180

                            196 - d² = 180    

                            d = 196 - 180 = 16

                            d = 4  

sum of the 7 terms = a-2d +a-d + a + a+d + a+2d + a+3d + a+4d

                               = 7a +7d

                               = 7(14+4) = 7(18) = 126