7th sum

Asked by lovemaan5500 | 2nd Feb, 2019, 08:26: PM

Expert Answer:

Let a be the first term and d be the common difference of an AP.
tp = a + (p - 1)d
tq = a + (q - 1)d
tr = a + (r - 1)d
According to the question terms are in GP
[a + (q - 1)d]2 = [a + (p - 1)d][a + (r - 1)d]
simplifying this we get
a = begin mathsize 16px style fraction numerator negative left parenthesis straight q squared minus 2 straight q minus pr plus straight p plus straight r right parenthesis straight d over denominator 2 straight q minus straight r minus straight p end fraction end style and r = begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style
Solving r = begin mathsize 16px style straight t subscript straight q over straight t subscript straight p end style
we get r = begin mathsize 16px style fraction numerator straight q minus straight r over denominator straight p minus straight q end fraction end style

Answered by Sneha shidid | 4th Feb, 2019, 01:04: PM